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

210

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=(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=
`(10!)/(4!(10-4!)=(10!)/(4!6!)`

Number o groups of 4 peoples=
`(10* 9* 8* 7* 6!)/(4* 3* 2* 1* 6!)=10* 3* 7=210`

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