Question

Find the number of combinations and permutations of 4 letters taken from the word examination'.

Answer 1

The number of combinations and permutations of 4 letters taken from the word examination is found as follows.

The word "examination" consists of 11 letters

 2 a's, 2 i's, 1 e, 1 x, 1 m, 1 t, 1 o.

The following combinations are possible:

1. 2 same, 2 same:³ C ₂ = 3 ways

The number of permutations = 3 × 4! / [2! × 2!] = 18

2. 2 same, 2 different: ³ C ₁ × ⁷ C ₂ = 63 ways

The number of permutations = 63 × 4! / 2! = 756

3. all 4 different: ⁸ C ₄ = 70 ways

The number of permutations = 70 × 4! = 1680

Hence required number of combinations = 3 + 63 +70 = 136.

Hence required number of permutations = 18 +756 +1680 = 2454.