SOLUTION: Three research departments have 7, 10, and 6 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how man

Question 1120931: Three research departments have 7, 10, and 6 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done?

Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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First department can choose the pair (delegate,alternate) by 7*6 = 42 ways.


Second department can choose the pair (delegate,alternate) by 10*9 = 90 ways.


Third department can choose the pair (delegate,alternate) by 6*5 = 30 ways.



Since these selections are INDEPENDENT,  the resulting choice can be done in 42*90*30 = 113400 ways.

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