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Nov 2014 p61 q7
2784
A committee of 6 people is to be chosen from 5 men and 8 women. One particular committee consists of 5 women and 1 man. In how many different ways can the committee members be arranged in a line if the man is not at either end?
Solution
First, arrange the 5 women. There are 5! ways to arrange them.
Next, consider the positions for the man. The man cannot be at either end, so he can be placed in any of the 4 middle positions.
Thus, the total number of arrangements is given by:
\(5! \times 4 = 120 \times 4 = 480\)
Alternatively, calculate the total number of arrangements of 6 people, which is 6!. Then subtract the cases where the man is at either end: