The correct options are
A m=41
B p=30
Given : 10∑j=0 30+jC10+j= mC20− pC21
Now,
10∑j=0 30+jC10+j= 30C10+ 31C11+ 32C12+⋯+ 40C20= 30C9+ 30C10+ 31C11+⋯+ 40C20− 30C9
Using nCr+ nCr−1= n+1Cr
= 41C20− 30C9
Therefore,
mC20− pC21= 41C20− 30C9⇒ mC20− pC21= 41C20− 30C21⇒m=41, p=30