Answer:
450 ways
Explanation:
Given that a mathematics exam consists of 10 multiple-choice questions and 5 open-ended problems in which all work must shown.
An examinee must answer 8 of the multiple-choice questions and 3 of the open-ended problems
8 multiple choice questions can be selected from 10 in 10C2 ways and 3 open ended problems in 5/c3 ways

In 450 ways the questions and problems can be chosen