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:

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

3 Girls and 4 boys are to be seated in a row on 7 chairs in such a way that all the three girls always sit together. In how many different ways can it be done?

In how many difference ways, can be letters of the word ‘CRISIS’ be arranged?

Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women.

A dice with numbers from 1 to 6 on its faces is thrown. If the outcome is an even number, it is thrown again, otherwise not. It is known that the dice was thrown for four times following this condition. In how many cases can the sum of numbers obtained in four throws be 16?

In how many ways can the letters of word COUSIN be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right?

There are two decks of 52 cards each. Two cards are to be selected from each deck. In how many ways the four cards can be selected such that the four cards are of different types (it means one is diamond, one is heart, one is spade and one is club)?

In how many different ways the word, TESTBOOK’ can be arranged so that vowels always come together?

For a chess team of 6 members, students are to be selected from 20 boys and 25 girls. However, the selected team should have at least two boys and at least two girls. Also, the number of boys and girls should not be equal. In how many ways can the team be selected?

A committee of 6 HODs is to be formed in a university out of 4 people from engineering department, 5 from management department and 3 from medical department. In how many ways the committee can be formed if two head of department from each department are to be included?

In how many different ways can 2 vowels and 3 consonants be selected from 4 vowels and 10 consonants?

Rohan decided to make collections of numbers greater than 0 and less than a million with the digits 0, 7 and 8. How many numbers are possible?

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