Question

There are 10 people in an office with 4 different phone lines. if all the lines begin to ring at once, how many groups of 4 people can answer these lines?

Answer 1

2 groups of 4 people can answer the different phone lines and 2 people will be leftover.

Answer 2

Answer:

210

Step-by-step explanation:

We are given that

Total number of peoples=n=10

Number of different phone lines=r=4

We have to find the number of groups of 4 people can answer 4 lines when all lines begin to ring at once.

Using combination formula

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

Substitute the values in the given formula

Then , we get number of groups of 4 people can answer 4 lines=$10C_4$

Number o groups of 4 peoples=$\frac{10!}{4!(10-4!}=\frac{10!}{4!6!}$

Number o groups of 4 peoples=$\frac{10\times 9\times 8\times 7\times 6!}{4\times 3\times 2\times 1\times 6!}=10\times 3\times 7=210$

Hence, 210 groups of 4 peoples can be made and answer these 4 lines.