SOLUTION: What is the coefficient of x^23 in the expression of (1 + x^5 + x^9)^100?

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Question 1206770: What is the coefficient of x^23 in the expression of (1 + x^5 + x^9)^100?
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


23 = 2(9)+1(5).

To get a partial product of x^23, you need to choose the x^9 term twice and the x^5 term one time, which means you need to choose the constant term 97 times. Since the coefficients of all the terms are 1, the coefficient of x^23 in the expansion is

100%21%2F%28%2897%21%29%282%21%29%281%21%29%29=%28100%2A99%2A98%29%2F2=485100

ANSWER: 485100