There are 8 ways to pick the first runner.
For each of those 8 ways to pick the 1st runner, there remain
7 way to pick the 2nd runner.
That's 8×7 or 56 ways to pick the 1st and 2nd runners
For each of those 8×7 or 56 ways to pick the first two runners, there
remain 6 way to pick the 3rd runner.
That's 8×7×6 or 336 ways to pick the 1st, 2nd, and 3rd runners.
For each of those 8×7×6 or 336 ways to pick the first three runners,
there remain 5 way to pick the 4th runner.
That's 8×7×6×5 or 1680 ways to pick the 1st, 2nd, 3rd, and 4th runners.
The answer is 8×7×6×5 = 1680 ways. That's also called the permutations
of 8 things chosen 4 at a time. It can be written P(8,4) or 8P4.
You can get it on a TI-83 or 84 calculator like this
press 8
press MATH
press the left arrow once
Press 2
Press 4
Press ENTER
you should read
8 nPr 4
1680
Edwin
