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?
32
48
36
60
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1
Discuss

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?
Solution 
2
Discuss

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?
Solution 
3
Discuss

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?
Solution 
4
Discuss

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?
Solution 
5
Discuss

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together
Solution 
6
Discuss

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?
Solution 
7
Discuss

In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Solution 
8
Discuss

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Solution 
9
Discuss

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?
Solution 
10
Discuss

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?
SolutionPerson will get profit of Rs 12 only when there is 2H (Head) and 1T (Tail) H + H + T = 12 8 + 8 + (4) = 12 Total outcome of 2 head and 1 tail = 2^{3} = 8 i.e (T, H, TH, HT, HH, HHT, HTH, THH) Total event with 2H and 1 T is 3 therfore probability = 3/8 
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