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Question

20r=0(20r)(3025r)=xCy, then find xy.

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Solution

Consider the following series.
mC0nCr+mC1nCr1+...mCrnC0
=Coefficient of xr in (1+x)m.(x+1)n
=Coefficient of xr in (1+x)m+n
=m+nCr
In the above case, r=25r+r=25 and m=20 and n=30
Hence
20+30C25=50C25
Hence 5025
=25.

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