Question

Ten teaching assistants are available for grading papers in a particular course. The first exam consists of four questions, and the professor wishes to select a different assistant to grade each question (only one assistant per question). In how many ways can assistants be chosen to grade the exam

Answer 1

There are 210 ways

Explanation:

The number of ways or combinations in which we can select x elements from a group of n elements where the order doesn't matter can be calculated as:

`nCx=(n!)/(x!(n-x)!)`

So, we have 10 teaching assistants and we need to choose 4 (one assistant per question) to grade each question. It means that n is equal to 10 and x is equal to 4.

Therefore, the number of ways that the assistants can be chosen to grade the exam are calculated as:

`10C4=(10!)/(4!(10-4)!)=210`