This unit has passed by so quickly! Combinatorics has been an interesting unit. Unlike the previous units, I think that this unit really had me because I can easily relate it to real life. :) The binomial theorem was what really amazed me (well, i think all of us did) the most. I couldn't imagine how numbers could be related in so many different ways! Ahh, the magic of numbers. (--,)

Anyway, here are some random things that I think we should not forget:

1. The number of ways you can arrange n things is n!

2. The pick formula is used when the position of something is taken into account to solve the problem.

3. If repetitions aren't allowed, we take the total number of ways you can arrange a group of things (k!) and then DIVIDE it by the number of ways you can arrange the things that are

repeated (m!). k!/m!

4. If repetitions are allowed, then just raise the thing to the power of how many times you need it.

5. If items should be together, take the items together as one item (p!), then find the number of ways that you can arrange them. Next, take the number of ways that you can arrange the items together (q!). Multiply the two. p!q!

6. The number of circular permutations is (n-1)!

7. The choose formula is used when the order of objects doesn't matter.

8. A deck of cards has 52 cards. 13 cards for each suit. 3 face cards for each suit. 4 of each card ( 4 aces, 4 two's...)

9. If a mixture of combinations is asked, take the ways you can choose one thing and another and then multiply them.

10. In the binomial theorem, the number of terms is equal to the power of the binomial PLUS one.

## Wednesday, May 13, 2009

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