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.