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:210Step-by-step explanation:We are given that Total number of peoples=n=10Number of different phone lines=r=4We 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 [tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]Substitute the values in the given formula Then , we get number of groups of 4 people can answer 4 lines=[tex]10C_4[/tex]Number o groups of 4 peoples=[tex]\frac{10!}{4!(10-4!}=\frac{10!}{4!6!}[/tex]Number o groups of 4 peoples=[tex]\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[/tex]Hence, 210 groups of 4 peoples can be made and answer these 4 lines.