find the coefficient of x^6 in (1 + x)^15

Question

Binomial Theorem.

Answer 1

(1 + x)¹⁵

From binomial theorem,

7^th term of expansion is 15c₆ 1^{15 - (7 - 1)} x^7-1

= 15c₆ 1⁹ x⁶

= 15c₆ x⁶

Now calculate 15c₆

15c₆ = (15 * 14 * 13 * 12 * 11 * 10 * 9!)/(9! * 6!)

= (15 * 14 * 13 * 12 * 11 * 10)/(6 * 5 * 4 * 3 * 2 * 1)

= (3603600)/(720)

= 5005.

The coefficient of x⁶ = 5005.