Question

There are 25 students in a science class. Twenty percent of the students are randomly selected to participate in a teacher evaluation. How many combinations of students are possible?

Answer 1

Answer: 53,130 possible combinations

Step-by-step explanation:

First, we want to find how much is the 20% of 25.

This is:

N = (20%/100%)*25 = 5.

So 5 students out of 25 are selected.

When we want to calculate the number of combinations of N elements it a group of K elements, we have:

$C = \frac{N!}{(N - K)!*K!}$

Here N = 25, and K = 5

$C = \frac{25!}{20!*5!} = \frac{25*24*23*22*21}{5*4*3*2*1} = 53,130$

so we have 53,130 combinations.