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

There are 2600 ways Mr. Pratt can choose three students to win the prizes.

Step-by-step explanation:

In Mr. Pratt's math class, there are 26 students. He wants to choose three students to win prizes: a pencil, an eraser, and a homework pass. The number of ways he can choose three students from 26 can be calculated using the combination formula:

C(n, r) = n! / (r!(n-r)!)

Using this formula, we can calculate:

C(26, 3) = 26! / (3!(26-3)!) = (26 x 25 x 24) / (3 x 2 x 1) = 2600

Therefore, there are 2600 ways Mr. Pratt can choose three students to win the prizes.

Answer 2

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}=(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}=(n!)/(k!(n-k)!)`

`=(26!)/(3!(26-3)!)`

`=(26!)/(3!* 23!)`

`=(26*25*24*23!)/(3!*23!)`

`=2600`

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