Question

White wolf is a horse in a race with 7 other runners. If we are concerned only with the first, second and third placings, in how many ways can white wolf finish first second and third?

Answer 1

126

Explanation:

If I understand the question correctly, we're looking for the number of ways that White Wolf can be 1st, 2nd, or 3rd, within a list of the top three placers.

This is a permutation question (we care about order):

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

If we set White Wolf as first, there are 2 other places we can look at:

`P_(7,2)=(7!)/(5!)=7xx6=42`

We add to this the number of ways White Wolf can be 2nd (which is also 42) and third (also 42), totalling `3xx42=126`