Question

Permutations formula

In how many different ways can five graduate students chose one of ten research projects, if not two of them can chose the same project?

Answer 1

To solve this problem, we can use the permutations formula. The answer is 30,240.

Step-by-step explanation:

To answer this question, we can use the concept of permutations. Since each student can choose a project in a different order, we need to find the number of ways they can choose projects without repetition.

The formula for permutations is nPr = n! / (n - r)!, where n is the total number of projects and r is the number of students. In this case, n = 10 and r = 5, so the formula becomes 10P5 = 10! / (10 - 5)! = 10! / 5! = 10 * 9 * 8 * 7 * 6 = 30,240.

Therefore, there are 30,240 different ways that the five graduate students can choose one of the ten research projects.