Question

solve it ..14th.... as soon as possible

Answer 1

Approach:

In the Sigma operator change the terms using C(n,r) = C(n, n-r).
We get n-r as 30 always.

So we have 12 terms in total on the LHS. In Each step Combine 2 terms from the left side. After 11 steps we get the answer.
.
Use this formula : C(n,r)+ C(n, r-1) = C(n+1, r)

C(40,31)+C(40,30)= C(41,31)
Add to C(41,30) to get C(42,31).
Continue. ...

So final answer C(51,31) or C(51,20).