Use the Permutations Formula
-The matching section of an exam has 5 questions and 7 possible answers. In how many different ways can a student answer the 5 questions, if none of the answer choices can be repeated?
A) 2520
B) 42
C) 21
D) 84

Question

Quizplus · Accepted Answer

This is a permutation problem because the order in which the answers are matched to the questions matters and no answer can be used more than once. The formula for permutations when choosing r items from a set of n items is nPr = n! / (n-r)!. Here, n = 7 (possible answers) and r = 5 (questions). So, 7P5 = 7! / (7-5)! = 7! / 2! = (7*6*5*4*3) / (2*1) = 2520.