SOLUTION: Show that C(n,r)= C(n-1,r-1)+C(n-1,r) NOTE: Professor said that you can start in either left side or right side

Question 970351: Show that C(n,r)= C(n-1,r-1)+C(n-1,r)

NOTE: Professor said that you can start in either left side or right side
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
by definition

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Replace every 'n' with 'n-1'. Replace every 'r' with 'r-1'

I'm going to call this equation Q

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Replace every 'n' with 'n-1'. I'm going to call this equation R

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we will use these ideas

to help us do the proof.

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Now onto the main proof. I'm only going to manipulate the right side of the equation to transform it into the left side.

Substitute equation Q and equation R (see above)

Use the tricks shown above (eg: to write as ).

I'm highlighting the common terms (shared between the fractions) in red

Factor out the common terms

So the identity is confirmed.
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