Question

select the correct answer.
at a high school there are 53 players on the football team, 15 players on the baseball team, and 12 players on the basketball team. how many ways can a committee be formed with 1 representative from each team?
a. 9540
b. 3,180
c. 8,162
d. 160

Explanation:

Step1: Apply multiplication principle

We use the multiplication principle of counting, which states that if there are $n_1$ ways to do one thing, $n_2$ ways to do a second thing, and $n_3$ ways to do a third thing, the total number of ways to do all three is $n_1 \times n_2 \times n_3$.
Here, $n_1=53$ (football players), $n_2=15$ (baseball players), $n_3=12$ (basketball players).

Step2: Calculate total combinations

$$53 \times 15 \times 12$$
First compute $53 \times 15 = 795$, then $795 \times 12 = 8162$.

Answer:

C. 8,162