Question

three research departments have 7, 9 and 8 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. I'm how many ways can this be done?

Answer 1

From the first department the possibility to select delegate is 7 and for alternate would be 6, so total ways for first department would be (7*6).

From the second department the possibility to select delegate is 9 and for alternate would be 8, so total ways for second department would be (9*8).

From the third department the possibility to select delegate is 8 and for alternate would be 7, so total ways for third department would be (8*7).

Total number of ways=(7*6)*(9*8)*(8*7)=169344