Tennis match - combinatorics A group organizing a faculty-student tennis match must match four faculty volunteers to four of the $13$ students who volunteered to be in the match. In how many ways can they do this? Is it just simply $13\choose4$ since the teachers is $4\choose4$? Thanks!

Line up the faculty members in order of seniority. The first faculty member can choose her opponent in $13$ ways. For **each** of these ways, the second most senior faculty member can choose her opponent in $12$ ways, and so on, for a total of $(13)(12)(11)(10)$.