The Math Department Has 6 Committees That Meet Once a Month

Essay

The Math Department has 6 committees that meet once a month. How many different meeting times must be used to guarantee that no one is scheduled to be at 2 meetings at the same time, if committees and their members are: $C _ { 1 } = \{$ Allen, Brooks, Marg $\} , C _ { 2 } = \{$ Brooks, Jones, Morton $\} , C _ { 3 } = \{$ Allen, Marg, Morton $\}$ , $C _ { 4 } = \{$ Jones, Marg, Morton $\} , C _ { 5 } = \{$ Allen, Brooks $\} , C _ { 6 } = \{$ Brooks, Marg, Morton $\}$ .