The question lends itself to the interpretation that we should calculate the number of combinations, assuming that the order in which she picks the 7 starters does NOT matter. However, an equally valid interpretation considering the real-world context would be that she is choosing her lineup with positions in mind. In that case, we would have to calculate permutations, since the order would matter (because she would be choosing one player as a goalie, the next as center forward, etc.) We can calculate both easily:
Combinations (order doesn't matter): Most calculators have a "choose" function, "nCr". We would type it in this way: 16 nCr 7. We have two different notations for this: 16C7 or a big pair of parentheses with 16 above and 7 immediately below. In either case, the formula is this: 16C7 = 16! / [(16 - 7)! · 7!] =
Permutations (order does matter): 16 nPr 7 = 16P7 = 16! / (16 - 7)! =
