Question

Mr. Pratt has 26 students in his math class. He has three prizes to give away: a pencil, an eraser, and a homework pass. How many ways can he choose three students to win these awards?

Answer 1

Answer:

Mr.Pratt can select three students to win these awards in 2,600 ways.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!(n-k)!}$

Mr. Pratt has three prizes to give away.

The total number of students in his class is, n = 26.

He has k = 3 prizes, namely a pencil, an eraser, and a homework pass.

Compute the number of combinations of three students Mr. Pratt can select from 26 students to give away the prizes as follows:

${n\choose k}=\frac{n!}{k!(n-k)!}$

     $=\frac{26!}{3!(26-3)!}$

     $=\frac{26!}{3!\times 23!}$

     $=\frac{26\times25\times24\times23!}{3!\times23!}$

     $=2600$

Thus, Mr.Pratt can select three students to win these awards in 2,600 ways.