Question

Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible? [Official GMAT-2018]

Hint:

When selecting items in a specific order, use the permutation formula \( P(n, r) = \frac{n!}{(n - r)!} \) to calculate the number of possible arrangements.

Answer 1

Step 1: Understand the problem.
Clarissa will randomly choose 4 books from 10 approved books, and the order in which the books are chosen matters. This is a permutation problem because the order of selection matters.
Step 2: Use the permutation formula.
The formula for the number of permutations of \( r \) objects from a set of \( n \) objects is: \[ P(n, r) = \frac{n!}{(n - r)!} \] In this case, \( n = 10 \) and \( r = 4 \), so: \[ P(10, 4) = \frac{10!}{(10 - 4)!} = \frac{10!}{6!} \] Simplifying the factorials: \[ P(10, 4) = 10 \times 9 \times 8 \times 7 = 5040 \] Step 3: Conclusion.
The total number of different lists that Clarissa can create is 5040.