Clarissa will create her summer reading list by randomly choosing 4 books from 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?

(A) 6

(B) 40

(C) 210

(D) 5,040

(E) 151,200

This is a basic permutation problem. For these and other basic counting problems – any combinatorics problem that doesn’t involve a combination (the selection of a subset without regard to order) – I use something I call “the blank method.”

I draw a blank for each choice. Here there are 4 choices, so I draw 4 blanks:

There are 10 possibilities for the first random choice.

10

There are 9 possibilities for the second random choice.

10 9

There are 8 possibilities for the third random choice and 7 possibilities for the forth random choice.

10 9 8 7

According to the fundamental principle of counting, the total number of lists is the product of these numbers:

\({10}\times{9}\times{8}\times{7} = {90}\times{56}\)

A good approximation for this is 5,000. The answer choices are so spread out that an approximation is more than sufficient here.

**The correct answer is D.**