Question

there are 20 students signed up to go on a field trip to the state capital. A group of 5 students will be chosen to personally meet the governor. How many different groups of 5 are possible?

Answer 1

To find this, we need to use combinations, since the order doesn’t matter.

This problem specifically is, “combinations of 20 pick 5”, which is shown below on the photo.
It is also written as shown by the arrow because the permutation (order does matter) of the same thing must be divided by the number of ways you could order the 5 students.

Multiply 20 x 19 x 18 x 17 x 16 on top. This is because there are 20 possibilities for the first student, and picking a student makes the possibilities for the next only 19.
Multiply 5 x 4 x 3 x 2 x 1 on the bottom for the same reason (this is also shown on the image below).

Simplify the top and bottom of the fraction. This is also shown on the image.

Then divide to get your final answer!

Answer: 15,504 combinations
Be sure to look at the attached image!

Hope this helps!