How many committees of five with a given chair person can be selected from 12 persons?

To form a committee of five with a designated chairperson from 12 persons, we first select the chairperson, which can be done in 12 ways. Once the chairperson is chosen, we need to select 4 additional members from the remaining 11 persons. This can be calculated using the combination formula (\binom{n}{k}), where (n) is the total number of persons remaining and (k) is the number of persons to choose. Thus, the total number of committees is (12 \times \binom{11}{4} = 12 \times 330 = 3960).