Fundamental principle of counting; permutation as an arrangement and combination as selection; meaning of P(n,r) and C(n,r); simple applications.
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Q1 · Permutations and Combinations · EASY
In how many ways can 5 boys and 3 girls be arranged in a row such that all the girls are together?
Q2 · Permutations and Combinations · MEDIUM
A committee of 5 members is to be formed from 6 men and 4 women. In how many ways can this be done if the committee must contain at least 2 women?
Q3 · Permutations and Combinations · MEDIUM
The number of ways in which 4 letters can be selected from the word 'EXAMINATION' is:
Q4 · Permutations and Combinations · EASY
How many 4-digit numbers greater than 5000 can be formed using the digits 3, 4, 5, 6, 7 without repetition?
Q5 · Permutations and Combinations · HARD
In how many ways can the letters of the word 'ARRANGE' be arranged such that the two R's are never together?