Determine the Appropriate Counting Technique to Use
-A poet will read 3 of her poems at an award ceremony. How many ways can she choose the 3 poems from 9 poems given that the sequence is important
A) 504
B) 60,480
C) 84
D) 120,960

Question

Quizplus · Accepted Answer

Since the sequence in which the poems are read is important, the appropriate counting technique to use is permutations. The number of ways to choose 3 poems out of 9 with regard to sequence is calculated using the permutation formula, which is $P(n, k) = \frac{n!}{(n-k)!}$. Here, $n = 9$ and $k = 3$, so $P(9, 3) = \frac{9!}{(9-3)!} = \frac{9!}{6!} = 9 \times 8 \times 7 = 504$.