Question

The number of selections of four letters from the letters of the word ASSASSINATION is –

• A. 72
• B. 71
• C. 66
• D. 52

Answer 1

Answer: (A)

72

Answer 2

There are 13 letters A, A, A; S, S, S, S; I, I; N, N; T; O

Coefficient of x⁴ in

(1 + x + x² + x³) (1 + x + x² + x³ + x⁴)

(1 + x + x²)² (1 + x)²

(Q 3A’s, 4S’s, 2I’s, 2N’s, 1 T and 1 O)

Ž Coefficient of x⁴ in

$\frac{(1 - x^{4})(1 - x^{5})(1 - x^{3})^{2}}{(1 - x)(1 - x)(1 - x)^{2}}$ (1 + x)²

Ž Coefficient of x⁴ in (1 + 2x + x² – 2x³ – 5x⁴) (1 – x)^–4

Ž Coefficient of x⁴ = 35 + 40 + 10 – 8 – 5 = 72 .