Our football team has 10 members, of which only 3 are strong enough to play offensive lineman, while all other positions can be played by anyone. In how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver?
One way to approach this problem is to first choose the offensive lineman, then choose the other positions. There are 3 ways to choose the offensive lineman, since there are 3 players who can play that position. After choosing the offensive lineman, we have 9 players left to choose from, and we can assign any of them to the remaining positions. There are 9 ways to choose the quarterback, since there are 9 players who can play that position. After choosing the quarterback, we have 8 players left to choose from, and we can assign any of them to the remaining positions. There are 8 ways to choose the running back, since there are 8 players who can play that position. After choosing the running back, we have 7 players left to choose from, and we can assign any of them to the remaining positions. There are 7 ways to choose the wide receiver, since there are 7 players who can play that position. To get the total number of ways to choose the starting lineup, we need to multiply the number of ways to choose each position, since they are independent events. The total number of ways is 3 x 9 x 8 x 7 = 1512. 