Question

A physics exam consists of 9 multiple-choice questions and 6 open-ended problems in which all work must be shown. If an examinee must answer 6 of the multiple-choice questions and 2 of the open-ended problems, in how many ways can the questions and problems be chosen?

Answer 1

The questions and problem can be chosen in 1260 ways.

Explanation:

Given that, a physics exam consists of 6 open-ended problem and 9 multiple choice questions.

The order of choosing does not matter.

So,we use combination to find ways.

The ways to choose 6 multiple choice from 9 is=
`^9C_6`

`=(9!)/(6!(9-6)!)`

=84

The ways to 2 open-ended question from 6 is=
`^6C_2`

`=(6!)/(2!(6-2)!)`

=15

Since pick 6 multiple choice out of 9 and 2 open-ended question out of 6 both are independent we have multiply both to find required ways.

Total number of ways is =(84×15)

=1260.