Permutations and Combinations

(continued)

Ah, good old permutations...well for now you are done with that.  Now you are on to combinations.

Remember the difference between them - permutations are when order matters (as in 123 is different from 321), and combinations are when order does not matter (as in ABC is the same as CBA).

The symbol for this is _nC_r

I'll give you the formula now...

_nC_r =_{_  n}P_{r  ___
               r}P_r

Oi, that is hard to read...basically it means _nC_r = _nP_r / _rP_r

Think of this...We have 3 cards, A, B, and C.  Now how many combinations of 2 of these cards can we make?

List them:
AB, AC
BC

That's it...because if we wrote BA (etc.), it would be the same as AB (after all order doesn't matter, they are both in the group).

Now use the formula. _nP_r =  ₃P₂ = 3 * 2 = 6
 _rP_r =  ₂P₂ = 2 * 1 = 2
6 / 2 = 3 combinations

How about this...a family of 5 people are going to a baseball game, but there are only 3 tickets left.  How many combinations of people could these tickets go to (assuming that they go to 3 of the family).

₅P₃ / ₃P₃ = (5 * 4 * 3) / (3 * 2 * 1) = 60 / 6 = 10 combinations

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