Saturday, December 13, 2008

How many? (4)

So, to recap -

A permutation is a grouping in which order matters (i.e. ABCDE is different from BACDE etc.).

The number of possible permutations of N things is N!
The number of possible permutations of N things selected from T things is T!/(T-N)!, or putting it more simply, the first N terms of T!

A combination is a grouping where order does not matter (i.e. ABCDE, BACDE and any other arrangement of the first five letters of the alphabet are considered the same group)

The number of combinations of N things selected from T things is T!/N!(T-N)!, or putting it more simply, the first N terms of T! divided by N! (or the first T-N terms of T! divided by (T-N)! - whichever is easier).

Just as a sideline, I hope those of you who have done the football pools and written "perm any 8 from 10" or some such, will now realise that this is not a permutation at all, but a combination - all that matters is which 8 games are chosen. Order is immaterial.

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