Quantitative Aptitude - Permutation & Combination - Formula & Concept Quiz

What is the sum of all 4 digit numbers that can be formed by the digits 1, 2, 3, 4 each exactly once

• 1]

  55566

• 2]

  66660

• 3]

  56456

• 4]

  84738

If P(A)=2/5​, P(B)=3/10​ and P(A ∩ B) =51​, then P(A' | B'). P(B' | A') is equal to

• 1]

  5/6

• 2]

  5/7

• 3]

  25/42

• 4]

  1

If A and B are two independent events with P(A) = 3/5 and P(B) = 4/9 , then P(A' ∩ B' ) equals

• 1]

  4/15

• 2]

  8/45

• 3]

  1/3

• 4]

  2/9

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B)=3/2​P(A) and P(C)=1/2​P(B), then P(A∪C)=

• 1]

  3/13

• 2]

  6/13

• 3]

  7/13

• 4]

  10/13

A biased coin in tossed thrice. What is the probability that heads turns out at least twice considering that the probability of a head is 60%?

• 1]

  0.648

• 2]

  0.234

• 3]

  0.348

• 4]

  .839

The value of  ⁷⁵P₂

• 1]

  5450

• 2]

  5555

• 3]

  5550

• 4]

  5656

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

• 1]

  40

• 2]

  400

• 3]

  5040

• 4]

  2520

In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

• 1]

  120

• 2]

  720

• 3]

  4320

• 4]

  2160

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together

• 1]

  10080

• 2]

  4989600

• 3]

  120960

• 4]

  None of these

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

• 1]

  63

• 2]

  90

• 3]

  126

• 4]

  45

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

• 1]

  159

• 2]

  194

• 3]

  205

• 4]

  209

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

• 1]

  32

• 2]

  48

• 3]

  36

• 4]

  60

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

• 1]

  32

• 2]

  48

• 3]

  64

• 4]

  96

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

• 1]

  266

• 2]

  5040

• 3]

  11760

• 4]

  86400

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated

• 1]

  5

• 2]

  10

• 3]

  15

• 4]

  20

In how many ways can the letters of the word 'LEADER' be arranged?

• 1]

  360

• 2]

  720

• 3]

  120

• 4]

  None Of These

How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.

• 1]

  17280

• 2]

  4320

• 3]

  720

• 4]

  80

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least three men are in the committee. In how many ways can it be done?

• 1]

  624

• 2]

  702

• 3]

  756

• 4]

  812

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

• 1]

  50400

• 2]

  2430

• 3]

  6540

• 4]

  12800

A box contains two white balls, three black balls and four red balls. Balls of the same colour are distinct. The number of ways in which three balls can be drawn from the box if atleast one black ball is to be included in the draw, is

• 1]

  32

• 2]

  64

• 3]

  128

• 4]

  None Of These

Three unbiased coins are tossed. What is the probability of getting at most two heads ?

• 1]

  3/4

• 2]

  1/4

• 3]

  3/8

• 4]

  7/8

In a simultaneous throw of two dice, what is the probability of getting a total of 7?

• 1]

  1/6

• 2]

  1/4

• 3]

  2/3

• 4]

  3/4

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

• 1]

  1/2

• 2]

  3/4

• 3]

  3/8

• 4]

  5/16

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

• 1]

  1/10

• 2]

  2/5

• 3]

  2/7

• 4]

  5/7

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?

• 1]

  5/13

• 2]

  10/13

• 3]

  1/13

• 4]

  1/26

From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being the Kings.

• 1]

  1/15

• 2]

  25/57

• 3]

  35/256

• 4]

  None Of These

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is

• 1]

  3/20

• 2]

  29/34

• 3]

  47/100

• 4]

  13/102

A box contains 5 green, 4 yellow and 3 white marbles. three marbles are drawn at random. What is the probability that all they are not of the same colour?

• 1]

  3/44

• 2]

  3/55

• 3]

  52/55

• 4]

  41/44

A speaks truth in 75% cases and B in 80% of the cases. In what percentage of the cases are they likely to contradict each other, narrating the same incident?

• 1]

  5%

• 2]

  15%

• 3]

  35%

• 4]

  45%

12 person are seated at a round table. Number of ways of selecting 2 persons not adjacent to each other is

• 1]

  10

• 2]

  11

• 3]

  54

• 4]

  48

If ,​, are probabilities of three mutually exclusive events, then

• 1]

  

• 2]

  

• 3]

  

• 4]

  None Of These

If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25 ?

• 1]

  0

• 2]

  1/2

• 3]

  1

• 4]

  1/1296

In a single throw with four dice,the probability of throwing seven is

• 1]

  20/6⁴

• 2]

  24/6⁵

• 3]

  22/8⁴

• 4]

  24/8⁴

A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

• 1]

  3/16

• 2]

  1/4

• 3]

  7/24

• 4]

  5/16

A coin is tossed 5 times. What is the probability that head appears an odd number of times?

• 1]

  1/2

• 2]

  2/3

• 3]

  1/3

• 4]

  1

Find the probability that a leap year selected at random will contain 53 Sundays

• 1]

  2/7

• 2]

  3/7

• 3]

  2/3

• 4]

  5/6

What is the probability of getting at least one six in a single throw of three unbiased dice?s

• 1]

  91/216

• 2]

  1/216

• 3]

  200/216

• 4]

  17/216

A person tosses an unbiased coin. When head turns up, he gets Rs.8 and tail turns up he loses Rs.4. If 3 coins are tossed, what is probability that he gets a profit of Rs.12?

• 1]

  3/8

• 2]

  5/8

• 3]

  3/4

• 4]

  1/8

The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is

• 1]

  185

• 2]

  175

• 3]

  115

• 4]

  105

In how many ways the letters of the word “UNDERDOG” can be arranged such that the first and last letters are same and no two vowels are together?

• 1]

  72

• 2]

  96

• 3]

  132

• 4]

  144

• 5]

  None of these

Three chairs are arranged in a row facing three other chairs. 4 boys and 2 girls are to be seated on these chairs such that girls are always facing each other. In how many ways can they be seated?

• 1]

  96

• 2]

  72

• 3]

  144

• 4]

  120

Six boys and 4 girls are to be seated in two separate rows with five chairs each, such that two particular girls are always together and all the girls are not in the same row. In how many ways can they be seated?

• 1]

  15 * 7!

• 2]

  20 * 8!

• 3]

  18 * 7!

• 4]

  (16 * 8! – 4! * 6!)

A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated?

• 1]

  10

• 2]

  18

• 3]

  36

• 4]

  12

Four letters are selected from the word “CAPAME” and are rearranged to form four letter words. How many words can be formed?

• 1]

  120

• 2]

  90

• 3]

  180

• 4]

  192

A basketball team of 5 players is to be selected from a group of 10 men and 8 women players. A volley ball team of 6 players is to be selected from a group of 8 men and 7 women players. Find the difference in the number of ways in which both the teams are selected, given that each team has only 2 female players.

• 1]

  1890

• 2]

  1920

• 3]

  1950

• 4]

  1990

Find the number of ways in which mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same game

• 1]

  1515

• 2]

  1500

• 3]

  1512

• 4]

  1550

If a team of 4 persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least 1 female

• 1]

  3500

• 2]

  1875

• 3]

  1750

• 4]

  3000

A committee of 8 members is to be selected from a group of 12 male and 10 female members. In how many ways the committee is selected such that at most two and at least one male member are there in the committee?

• 1]

  13540

• 2]

  14200

• 3]

  15300

• 4]

  16400

A five-letter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed?

• 1]

  40

• 2]

  42

• 3]

  45

• 4]

  52

A polygon has 44 diagonals. What is the number of its sides?

• 1]

  7

• 2]

  8

• 3]

  9

• 4]

  11

How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?

• 1]

  42

• 2]

  294

• 3]

  315

• 4]

  258

A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?

• 1]

  12

• 2]

  10

• 3]

  8

• 4]

  6

How many four-digit numbers, each divisible by 4 can be formed using the digits 5, 6, 7, 8, 9, repetition of digits being allowed in any number?

• 1]

  75

• 2]

  100

• 3]

  125

• 4]

  150

There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?

• 1]

  12

• 2]

  13

• 3]

  17

• 4]

  18

How many 5 digit even numbers with distinct digits can be formed using the digits 1, 2, 5, 5, 4?

• 1]

  16

• 2]

  24

• 3]

  36

• 4]

  48

There are three rooms in a motel: one single, one double, and one for four persons. How many ways are there to house seven persons in these rooms?

• 1]

  7! / 1! 2! 3! 

• 2]

  7! 

• 3]

  7! / 3

• 4]

  7! / 3!

If C(n, 7) = C(n, 5), find n

• 1]

  12

• 2]

  15

• 3]

  18

• 4]

  -1

There are 8 orators A, B, C, D, E, F, G, and H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.

• 1]

  8! / 3!

• 2]

  8! / 6!

• 3]

  5! x 3!

• 4]

  8! / (5! x 3!) 

If ¹⁸C_r = ¹⁸C_r+2 ; find ^rC₅.

• 1]

  56

• 2]

  63

• 3]

  49

• 4]

  42

The number of circles that can be drawn out of 10 points of which 7 are collinear is

• 1]

  130

• 2]

  85

• 3]

  45

• 4]

  72

How many rectangles can be formed out of a chess board ?

• 1]

  1740

• 2]

  1230

• 3]

  1296

• 4]

  204

How many natural numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?

• 1]

  496

• 2]

  728

• 3]

  486

• 4]

  1084

One red flower, three white flowers, and two blue flowers are arranged in a line such that
I. No two adjacent flowers are of the same color.
II. The flowers at the two ends of the line are of different colors.
In how many different ways can the flowers be arranged?

• 1]

  2

• 2]

  4

• 3]

  6

• 4]

  10

Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done

• 1]

  2 x ¹²C₆ x (6!)²

• 2]

  2 x 6! x 6!

• 3]

  2 x ¹²C₆ x 6!

• 4]

  None of these

A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is

• 1]

  7

• 2]

  8

• 3]

  9

• 4]

  24

How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place?

• 1]

  60

• 2]

  54

• 3]

  51 / 3

• 4]

  2 x 4!

There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?

• 1]

  120

• 2]

  130

• 3]

  100

• 4]

  110

From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?

• 1]

  1360

• 2]

  1060

• 3]

  1160

• 4]

  1260

The students in a class are seated, according to their marks in the previous examination. Once, it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate bits of paper in order to choose one of these by lots. How many bits of paper are required?

• 1]

  24

• 2]

  12

• 3]

  36

• 4]

  48

In how many ways can a cricketer can score 200 runs with fours and sixes only?

• 1]

  13

• 2]

  19

• 3]

  16

• 4]

  17

There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters.

• 1]

  2! x 19!

• 2]

  18!

• 3]

  18! x 2!

• 4]

  19!

Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?

• 1]

  36

• 2]

  84

• 3]

  180

• 4]

  381

How many integers between 1000 and 10000 have no digits other than 4, 5, or 6?

• 1]

  91

• 2]

  71

• 3]

  51

• 4]

  81

A number lock on a suitcase has 3 wheels each labeled with 10 digits from 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?

• 1]

  720

• 2]

  760

• 3]

  780

• 4]

  680

If (n + 2)! = 2550 (n!); find ’n’

• 1]

  49

• 2]

  35

• 3]

  38

• 4]

  43

In how many ways can 10 people line up at a ticket window of a railway station?

• 1]

  36,28,800

• 2]

  34,82,800

• 3]

  33,44,800

• 4]

  33,28,800

How many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once?

• 1]

  38,320

• 2]

  39,320

• 3]

  38,400

• 4]

  40,320

Ten participants are participating in a competition. In how many ways can the first three prizes be won?

• 1]

  920

• 2]

  680

• 3]

  720

• 4]

  820

It is required to seat 5 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?

• 1]

  2880

• 2]

  2148

• 3]

  3280

• 4]

  3680