Everybody in a room shakes hands with everybody else. The total number of hand-shakes is 55. The total number of persons in the room is:

There are four different bags. Also, there are four different coins. In how many ways can the coins be put into bags if there are exactly two coins in exactly one of the bags?

If four coins are tossed together, what is the probability of at least getting 2 heads?

In how many different ways can the letters of the word ‘DESIGN’ be arranged so that the vowels are at the two ends? 

Out of 5 men and 3 women. committee of 3 members is to be formed so that it has 1 woman and 2 men. In how many different ways can it be done? 

In how many different ways can the letters of the word ‘CREAM’ be arranged?

In how many different ways can the letters of the word ‘STRESS’ be arranged?

In how many different ways can letters of the word ‘SECOND’ be arranged?