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Question

If 10j=0 30+jC10+j= mC20 pC21, then

A
m=41
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B
p=30
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C
m=40
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D
p=31
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Solution

The correct options are
A m=41
B p=30
Given : 10j=0 30+jC10+j= mC20 pC21
Now,
10j=0 30+jC10+j= 30C10+ 31C11+ 32C12++ 40C20= 30C9+ 30C10+ 31C11++ 40C20 30C9
Using nCr+ nCr1= n+1Cr
= 41C20 30C9
Therefore,
mC20 pC21= 41C20 30C9 mC20 pC21= 41C20 30C21m=41, p=30

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