SOLUTION: Seven prizes are to be given to seven different people in a group of fourteen. In how many ways can a first prize, a second prize, a third prize and four fourth prizes be given?
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Question 1125006: Seven prizes are to be given to seven different people in a group of fourteen. In how many ways can a first prize, a second prize, a third prize and four fourth prizes be given? Answer by ikleyn(52797) (Show Source):
There are 14 ways to select the first person for the first prize.
There are 13 ways to select the second person from 13 remaining for the second prize.
There are 12 ways to select the third person from 12 remaining for the third prize.
There are ways to select the group of 5 persons for fourth prizes .
is the number of combinations of 11 items taken 5 at a time
= = 462.
In all, there are 13*12*11*462 = 792,792 ways to do it.
