Question

The Taney Dragons are going to the Little League World Series! In appreciation, each of the 12 distinct team members (players) can pick 2 hats from a supply of red (Philly Phillies), blue (Boston Red Sox), and green (Ploiesti Frackers) hats. For each color, the supply is unlimited. In how many di erent ways can the hat picking for the whole team be done

Answer 1

Answer:

The hat picking can be done in 36 different ways for the whole team.

Step-by-step explanation:

For each player, the order in which they pick the hats is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

For each player:

2 hats from a set of 3. So

$C_{3,2} = \frac{3!}{2!(3-2)!} = 3$

12 players:

So in total, there are 12*3 = 36 different ways.

The hat picking can be done in 36 different ways for the whole team.