Eight people audition for a choir. The choir director must choose one soprano, one alto, and one tenor. In how many ways can the director fill these
positions
A. 56
B. 336
C. 6720
D. 40,320

Question

Eight people audition for a choir. The choir director must choose one soprano, one alto, and one tenor. In how many ways can the director fill these
positions 
A. 56 
B. 336 
C. 6720 
D. 40,320

1davey29 · Answer

To solve this, use the combination formula $$C _{r}^{n}=\frac{ n! }{ (r!)((n-r)!) }$$ n representing your total number in your set, 8 in your case, and r representing the size of the group you need to pick, 3 in your case.