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?
2
4
6
10
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1
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 
2
Discuss

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together
Solution 
3
Discuss

There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?
Solution 
4
Discuss

If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25 ?
Solution 
5
Discuss

In a simultaneous throw of two dice, what is the probability of getting a total of 7?
Solution 
6
Discuss

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?
Solution 
7
Discuss

From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being the Kings.
Solution 
8
Discuss

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?
Solution 
9
Discuss

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

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?
Solution 
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