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Coach Grunt is preparing the 5-person starting lineup for his basketball team, the Grunters. There are 12 players on the team. Two of them, Ace and Zeppo, are league All-Stars, so they'll definitely be in the starting lineup. How many different starting lineups are possible? (The order of the players in a basketball lineup doesn't matter.)

ant101  Feb 18, 2018
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Well ....two of the positions are "set"

So.....  we just want to choose any 3 of the remaining  10 players  = C(10,3)  = 120  different lineups

CPhill  Feb 18, 2018
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Coach Grunt has to choose 3 players from the 10 players that are remaining after Ace and Zeppo have been placed in the lineup. The order in which the players are chosen doesn't matter, so the answer is $$\binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = \boxed{120}.$$

azsun  Feb 18, 2018
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