Solutions to Practice Problems for  the Lander Math Contest
Module 9, Solutions (26-28)

The order of the chosen people in this problem does not
matter, so we count the number of combinations:

27) Two “words” with same letters but different order are
different, that is why we will calculate the number of
permutations (when order matters):

28) Let us divide the number of permutations by the number
of combinations:
nPk÷nCk = n!/(n-k)!÷n!/[(n-k)!k!]= n!/(n-k)!× [(n-k)!k!]/n!=k!