Question

Can somebody help me re-learn combinations and permutations? I haven't used them in years and I'm taking the GRE in the next month!

Answer 1

do you have a specific question? it is easy enough to write a formula, but that might not be helpful

Answer 2

Well, I don't have any specific questions. It's just that I can't just memorize the formulas without fully understanding them.

Answer 3

ok well if you want "permutations" like arranging 4 people in 4 chairs, the number of ways to do it is
\[4!=4\times 3\times 2\] and that is simple enough to understand by the "counting principle"
4 choices for the first seat
3 for the second
2 for the third
and no choice for the last one

Answer 4

Yeah, I understand that.. But then once I get to combinations, I get confused.

Answer 5

http://www.khanacademy.org/video/permutations?playlist=Precalculus

Answer 6

Seriously. Go there.

Answer 7

Watch that video and the ones that follow.

Answer 8

oh ok well if you understand that, then we are on our way. suppose then you want to know how many committees of 4 people you can make out of a total of ten people. then again by the counting principle you have

\[10\times 9\times 8\times 7\] ways to do it, but that counts too many because it counts all the permutations as different. so you have to divide by the number of ways you can permute the 4 people, and we just said what that way, namely 4!

Answer 9

so the answer would be
\[\frac{10\times 9\times 8\times 7}{4\times 3\times 2}\]

Answer 10

ok

Answer 11

what about if repetitions are allowed?