I have to show the following: C(n,0) + C(n+1,1) + ...+ C(n+r,r)= C(n+r+1,r) The

Question

I have to show the following:

C(n,0) + C(n+1,1) + ...+ C(n+r,r)= C(n+r+1,r)

The original problem is written the other way combinations are written as but the equation didn't show up correctly so I used this alternatively.

Also, anyone have any advice for solving permuations and combinations problems? For some reason I cannot seem to grasp these concepts fully. I understand the broad scheme but when I am faced with problems, I freeze because I feel like I don't know what to do. Anything that could make it easier to understand these problems fully would be greatly appreciated especially since my whole class is applied combinatorics. Thanks.

Explanation / Answer

C(n,r) = n!/(n-r)!r! C(n,0) + C(n+1,1) + ...+ C(n+r,r) =1+(n+1)!/(n)!1!+......+(n+r)!/(n)!r! =1+(n+1)+...+(n+r)!/(n)!r! =C(n+r+1,r)

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