What type of equations are these? I have never seen such questions. Please explain the equation and solve it too.

No links please

Dear Student

The following equation represents a binomial distribution which can written as 

Crn or nr
Given500501+501502+........50495050Using nr=nn-r----(i)The above expansion can be expressed as 50k50k+1k=049Now using Vandermonde's identitym+nr=  mkk=0rm+nr50k5049-k=k=04950+5049=10049Using (i) we get5049-k=50k+110049=10051

Kindly request you to post the other questions in different thread
Regards

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Dear student, these questions are from permutation and combination, and thus, could be rewritten as:

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What are you looking for?