An accounting firm is selecting three accounts to audit out of a total of 11 accounts. The number of ways the firm can select the three accounts is given by $11 \cdot 10 \cdot 9$.

Question

Quizplus · Accepted Answer

The correct number of ways to select three accounts out of 11 is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items, $k$ is the number of items to choose, and $n!$ denotes the factorial of $n$. For this case, it is $C(11, 3) = \frac{11!}{3!(11-3)!} = \frac{11!}{3!8!}$, which simplifies to $\frac{11 \cdot 10 \cdot 9}{3 \cdot 2 \cdot 1}$, not $11 \cdot 10 \cdot 9$.

An Accounting Firm Is Selecting Three Accounts to Audit Out 11⋅10⋅911 \cdot 10 \cdot 911⋅10⋅9

An Accounting Firm Is Selecting Three Accounts to Audit Out $11 \cdot 10 \cdot 9$