Use the Combinations Formula
-Ron finds 8 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how many ways can he make his selection? How many ways can he make his selection if he decides that one of the books is a must?
A) 56; 35
B) 6720; 840
C) 336; 210
D) 3360; 420

Question

Quizplus · Accepted Answer

The number of ways to choose 5 books out of 8 is calculated using the combinations formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. So, for choosing 5 out of 8, it's C(8, 5) = 8! / [5!(8-5)!] = 56. If one book is a must, then he is choosing 4 out of the remaining 7, which is C(7, 4) = 7! / [4!(7-4)!] = 35.