# Trouble understanding combinations

• Apr 13th 2010, 07:39 AM
nightrider456
Trouble understanding combinations
I'm having trouble understanding this, any explaination or info would be great.

Jane calculated 10C2 to be 45 arangements. she then calculated 10C8 to be 45 arrangements
A.) explain in words why 10C2=10C8
B.) prove the identity nCr= nCn-r
• Apr 13th 2010, 02:05 PM
awkward
Quote:

Originally Posted by nightrider456
I'm having trouble understanding this, any explaination or info would be great.

Jane calculated 10C2 to be 45 arangements. she then calculated 10C8 to be 45 arrangements
A.) explain in words why 10C2=10C8
B.) prove the identity nCr= nCn-r

Suppose you have 10 shirts, all different. When you take 2 shirts out of your closet, you are leaving 8 shirts behind. If you know the 8 shirts left behind, you have uniquely identified the 2 you took out; and if you know the 2 you took out, you know exactly which set of 8 you left behind. So there are exactly as many ways to take out 2 shirts as there are ways to to leave 8 behind.

Put more abstractly, there is a one-to-one correspondence between subsets of size 2 taken from a set of size 10 and subsets of size 8 taken from the same set.