Question

There are 17 people in an office with 5 different phone lines. If all the lines begin to ring at once, how many groups of 5 people can answer these lines?

Answer 1

Answer:

6188 different combinations of people

Step-by-step explanation:

This is a combination problem since it does not matter the order of people that answer the phones.  The combination looks like this:

₁₇C₅ = $\frac{17!}{5!(17-5)!}$

This expands to

$\frac{17*16*15*14*13*12!}{5*4*3*2*1(12!)}$

The 12! cancels out in the top and bottom so the remaining multiplication leaves you with

₁₇C₅ = $\frac{742560}{120}$

which divides to 6188