SOLUTION: Five prizes are to be given to five different people in a group of seventeen. In how many ways can a first prize, a second prize, a third prize and two fourth prizes be given?

Question 996826: Five prizes are to be given to five different people in a group of seventeen. In how many ways can a first prize, a second prize, a third prize and two fourth prizes be given?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

Choose the first prize winner as any one of 17 people.
Choose the second prize winner as any one of the 
remaining 16 people.
Choose the third prize winner as any one of the 
remaining 15 people.
Choose the two fourth prize winners as any combination
of 2 of the remaining 14 ways.  That's 14C2.

Answer: (17)(16)(15)(14C2) = 371280

Edwin

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