quite ‘small’ configurations give rise to ‘large’ factorial numbers. The number n
may be small but n! can be huge.
If we’re still interested in forming queues of 5 people, but can now draw on a
pool of 8 people A,B, C, D, E, F, G, and H, the analysis is almost the same.
There are 8 choices for the front person in the queue, 7 for the second and so
on. But this time there are 4 choices for the last slot. The number of possible
queues is
8 × 7 × 6 × 5 × 4 = 6720
This can be written with the notation for factorial numbers, because
Combinations
In a queue the order matters. The two queues number factorial
C E B A D D A C E B
are made from the same letters but are different queues. We already know
there are 5! queues that can be made with these letters. If we’re interested in
counting the ways of selecting 5 people from 8 immaterial of order we must
divide 8 × 7 × 6 × 5 × 4 = 6720 by 5!. The number of ways of selecting 5
people from 8 is therefore