Find-the-coefficient-of-x-18-in-expression-1-x-3-x-5-x-7-100-

Question Number 191177 by naka3546 last updated on 19/Apr/23

Find the coefficient of x^{18} in expression

{(1 + x^{3} + x^{5} + x^{7})}^{100} .

Answered by mehdee42 last updated on 19/Apr/23

(_{94, 6}^{100}) + (_{96, 2, 1, 1}^{100}) + (_{96, 1, 3}^{100}) = \frac{100!}{94! 6!} + \frac{100!}{96! 2!} + \frac{100!}{96! 3!}

Commented by naka3546 last updated on 19/Apr/23

Thank you