Abhijit Guha Solutions for Chapter: Permutation and Combination, Exercise 1: Practice Problems Level 1

How many different words can be formed with five given letters of which three are vowels and two are consonant no two being together in any words?

In how many ways $5$ boys and $4$ girls be seated in a round table if there is no restriction?

There are $5$ boys and $4$ girls be seated at a round table. In how many ways that all the $4$ girls sit together?

There are $5$ boys and $4$ girls be seated at a round table, In how many ways $4$ girls do not sit together?

In how many ways $5$ boys and $4$ girls are seated in a round table such that no two girls sit together?

A round table conference is to be held between $10$ delegates of $10$ countries. In how many ways can they be seated if two particular delegates are always to sit together?

$4$ gentlemen and $4$ ladies are invited to a certain party. In how many ways they can be seated at a round table so that only ladies are seated on the two sides of each gentlemen?

In how many ways can $6$ person sits around a table so that all shall not have the same neighbours in any two arrangements?