Unformatted text preview: Consider the following problem: 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? Since it does not matter which line gets picked up ﬁrst, the given problem is a combination. Remember that a combination is used when order is not important. Written symbolically,
C = —.
n r r! ( n — r )! Therefore, we will have 16C5 combinations of 5 phone lines being answered by 16 people. Solving for the number of ways we can have 5 phone lines answered, we get 16! 16! 20922789888000
C — — — 4368. ‘55 5!(16—5)! 5!11! (120)(39916800) ...
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- Spring '10