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?A. 6B. 40C. 210D. 5,040E. 151,200

Answer 1

Answer: D. 5040

Step-by-step explanation:

Given : The total number of books = 10

The number of books required by Clarissa = 4

Now , when we select r things from n things and order in which they are chosen matters then we use permutations to calculate the number of  different lists are formed to choose them.

The number of permutations of n things taking r at a time is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

For r= 4  and n= 10 , we have

$^{10}P_{4}=\dfrac{10!}{(10-4)!}\\\\=\dfrac{10\times9\times8\times7\times6!}{6!}=10\times9\times8\times7=5040$

Hence, the number of different lists are possible = 5040

Therefore , the correct answer = D. 5040