Question

Our football team needs to fill 4 positions. To do this, it 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?

Answer 1

There are 1,512 different ways to fill the positions.

For each spot, we need to determine the number of players that can fill the spot. Then, multiply them together.

For the offensive lineman, there are only 3 choices. After that, we start with 9 players, then 8 and finally 7.

3 x 9 x 8 x 7 = 1512