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Permutation and Combination

Counting, arrangements, selections — basic level for Prelims.

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Q1 · Permutation and Combination · EASY
In how many different ways can the letters of the word 'PAPER' be arranged?
Q2 · Permutation and Combination · MEDIUM
A committee of 4 members is to be formed from 6 men and 5 women. In how many ways can the committee be formed if it must contain at least 2 women?
Q3 · Permutation and Combination · EASY
How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 without repetition such that the number is divisible by 5?
Q4 · Permutation and Combination · MEDIUM
In how many ways can 5 boys and 3 girls be seated in a row such that no two girls sit together?
Q5 · Permutation and Combination · HARD
A bag contains 5 red balls, 4 blue balls, and 3 green balls. In how many ways can 4 balls be selected such that at least one ball of each colour is selected?