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The coefficient of $x^{7}$ in the expansion of ${(1 + \frac{1}{1!} x + \frac{1}{2!} x^{2} + \frac{1}{3!} x^{3} + \frac{1}{4!} x^{4} + \frac{1}{5!} x^{5})}^{2}$ is

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27! 8C3

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detailed solution

Correct option is A

Required coefficient is12!5!+13!4!+14!3!+15!2!=17! 7C2+7C3+7C4+7C5=27! 7C2+7C3=27! 8C3

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The coefficient of x7 in the expansion of 1+11!x+12!x2+13!x3+14!x4+15!x52is

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The coefficient of $x^{7}$ in the expansion of ${(1 + \frac{1}{1!} x + \frac{1}{2!} x^{2} + \frac{1}{3!} x^{3} + \frac{1}{4!} x^{4} + \frac{1}{5!} x^{5})}^{2}$ is