Our basketball team has 12 members, each of whom can play any position.  In how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard?
There are 12 choices for the first position, then 11 players to choose from for the second, then 10 for the third, then 9 for the fourth, and finally just 8 for the fifth, for a total of $ 12 \times 11 \times 10 \times 9 \times 8 = \boxed{95,\!040}$.
95040
Level 4
Prealgebra
Problem: Our basketball team has 12 members, each of whom can play any position.  In how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the number of ways to choose a starting lineup from 12 basketball team members, we need to consider the positions required: center, power forward, shooting forward, point guard, and shooting guard. This totals 5 distinct positions.

First, we select a player for the center position. There are 12 possible choices since all team members are eligible. After selecting the center, we have 11 remaining players to choose from for the power forward position. 

Next, for the shooting forward position, we have 10 players left after choosing the center and power forward. For the point guard position, we will have 9 players remaining. Finally, for the shooting guard position, we will have 8 players left to choose from.

The total number of ways to select the starting lineup can be calculated by multiplying the number of choices for each position:

Total ways = (choices for center) × (choices for power forward) × (choices for shooting forward) × (choices for point guard) × (choices for shooting guard)

This can be expressed mathematically as:

Total ways = 12 × 11 × 10 × 9 × 8

Now, we perform the multiplication step-by-step:

1. 12 × 11 = 132
2. 132 × 10 = 1320
3. 1320 × 9 = 11880
4. 11880 × 8 = 95040

Thus, the final answer is 95040.<|END_OF_LATENT|> The final answer is $95040$.