Selections with conditions

In a team with equal roles, the order in which names are written does not produce another team. Use combinations within each specified category. A committee of three chosen from four musicians and five athletes, containing exactly one musician, has 41 52=40 possibilities. The multiplication joins independent selections; it does not assign roles. For at least one musician, subtract the no-musician case: 93- 53=74. Alternatively add the mutually exclusive one-, two- and three-musician cases. For an unknown group size, translate the count into an equation. If n2=28, then n(n-1)=56, giving n=8 or n=-7. A number of people must be a non-negative integer, so only n=8 is valid.