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Question

The coefficient of x2y3 in the expansion of (1x+y)20 is

A
20!2!3!
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B
20!2!3!
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C
20!5!2!3!
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D
none of these
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Solution

The correct option is B none of these
(1x+y)20=(20)!(r1)!(r2)!(r3)!{1r(x)r2(y)r3}
r1+r2+r3=20
To find the coefficient of x2y3
r2=2:r3=3
& r1=20(2+3)=15
Coefficient =20!(15!)(2!)(3!)
Hence, the answer is none of these.

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