Question

There are 11 people in an office with three different phone lines. If all the lines begin to ring at once how many groups of three people can answer these lines

Answer 1

ANSWER:

165 different groups

STEP-BY-STEP EXPLANATION:

Since either person can answer any phone, no matter what order, we use the following combination formula:

$_nC_r=\frac{n!}{r!(n-r)!}$

In this case, n is equal to 11 and r = 3, therefore:

$\begin{gathered} _{11}C_3=\frac{11!}{3!(11-3)!}=\frac{11!}{3!\cdot8!} \\ \\ _{11}C_3=165 \end{gathered}$

This means that 165 different groups of three people can answer these lines