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Question

The coefficient of x2y3 in the expansion of (1x+y)20 is
  1. 20!2!3!
  2. 20!2!3!
  3. 20!(15!)(3!)(2!)
  4. 20!5!2!3!


Solution

The correct option is C 20!(15!)(3!)(2!)
The general term in the expansion of (1x+y)20
=20!k1!k2!k3!1k1(x)k2(y)k3

Where, k1+k2+k3=20
For x2y3, so
k2=2,k3=3k1=15 

Hence, the coefficient of x2y3
=20!(15!)(3!)(2!)

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