Permutations And Combinations

A coach needs to select a $\mathbf{4}$-player starting lineup from a pool of $\mathbf{1 0}$ players:

• 5 guards




• 3 forwards




• 2 centres

Find the number of different selections if the 4-player starting lineup must include:

• At least 1 guard




• At most 1 forward




• Exactly 1 centre