Set II, Combinations

After checking Set I, we moved into Set II together today... working all the way up until the last four or five problems.  Their job is to get those last 4-5 done before 11:20AM on Monday. :)

An aside, the kids have really got to nail down the relationship between (1) The Fundamental Counting Principle, (2) Permutations, and (3) Combinations.

In particular, today it was revealed that some folks don't remember what nPr and nCr mean (permutations and combinations, respectively).  I'll try to explain here.

nPr = n -- the number of total "things" taken r at a time

So, 9P2 (pretend the 9 and 2 are subscripts) = 9 * 8 (start at 9, go down two, multiply) = 72

Well, nCr = nPr/r!

So, 9C2 = (9*8)/2!

Remember that "!" in math does not mean what it does in the English language. :)  ! means factorial, or take this example:

5! = 5 * 4 * 3 * 2 * 1

Whew.  Make sense???  Ha!

Try this out