Question

A man is planning for college and takes a standardized test. While registering for the​ test, he is allowed to select two schools to which his scores will be sent at no cost. If there are 11 colleges he is​ considering, how many different ways could he fill out the score report​ form?

Answer 1

The total number of ways he fill out the score report​ form is 55.

Explanation:

Consider the provided information.

There are 11 colleges he is​ considering, he is allowed to select 2 schools to which his scores will be sent at no cost.

Out of 11 colleges he can only select 2 schools that means order doesn't matter.

According to the definition of combination:
`^nC_r=(n!)/(r!(n-r)!)`

Substitute n = 11 and r = 2 in above formula

Therefore, the number of possible ways are:

`^(11)C_2=(11!)/(2!(11-2)!)`

`^(11)C_2=(11!)/(2!(9)!)`

`^(11)C_2=55`

Hence, the total number of ways he fill out the score report​ form is 55.