Seven women and nine men are on the faculty in the mathematics department. How many ways are there to select a committee of five members of the department if at least one man must be in the committee?
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Step 1: Calculate the total number of ways to select a committee of 5 members from 16 total members (7 women and 9 men) using the combination formula: \[ \binom{16}{5} = 4368 \] Show more…
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Seven women and nine men are on the faculty in the mathematics department at a school. a) How many ways are there to select a committee of five members of the department if at least one woman must be on the committee? b) How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee?
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