Question

There are 6 athletes on a chess team. At a photoshoot, 4 of the athletes need to be chosen and arranged in the front row. In how many ways can this be done?

Answer 1

There are 360 different ways to choose and arrange 4 athletes from a team of 6 in the front row, done by calculating permutations using the formula P(6,4) = 6! / (6-4)!, which equals 360.

Step-by-step explanation:

To determine in how many ways 4 athletes can be chosen and arranged in the front row from a team of 6, we use the concept of permutations. Permutations are used because the order of the athletes matters in this context. The formula for permutations is given by P(n,r) = n! / (n-r)!, where 'n' is the total number of items to choose from, 'r' is the number of items to choose, and '!' represents the factorial function.

In this case, we need to calculate P(6,4), which corresponds to 6! / (6-4)!.

1. Firstly, calculate the factorial of 6: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
2. Secondly, calculate the factorial of (6-4), which is 2! = 2 x 1 = 2.
3. Finally, divide the factorial of 6 by the factorial of 2 to get the number of permutations: 720 / 2 = 360.

Therefore, there are 360 different ways for the athletes to be chosen and arranged in the front row.