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

$$\mathrm{Find}\mathrm{the}\mathrm{coefficient}\mathrm{of}{x}^{18}\mathrm{in}\mathrm{expression}$$$${(1+x^3+x^5+x^7)}^{100}.$$

Answered by mehdee42 last updated on 19/Apr/23

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

Commented by naka3546 last updated on 19/Apr/23

$$\mathrm{Thank}\mathrm{you}$$

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