There are 16
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?
This is a combination problem, where order does not matter. We can calculate this using the combination formula:
C(n, k) = n! / (k! * (n - k)!)
Where n is the total number of people and k is the number of people we want to choose.
Plugging in the numbers:
C(16, 5) = 16! / (5! * (16 - 5)!)
= 16! / (5! * 11!)
= 4368
Therefore, there are 4368 different groups of 5 people that can answer the 5 phone lines.