SOLUTION: Six prizes are to be given to six different people in a group of ten. In how many ways can a first prize, a second prize, a third prize and three fourth prizes be given?
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Question 1168539: Six prizes are to be given to six different people in a group of ten. In how many ways can a first prize, a second prize, a third prize and three fourth prizes be given? Answer by math_helper(2461) (Show Source):
It is the same as the number of ways a 1st,2nd,and 3rd prize can be assigned to 6 different people (i.e. we can ignore the three fourth place prizes, as they simply fall into place after the first three prizes are given):
First choose 3 people from 6: 6C3 = 6!/((6-3)!3!) = 6*5*4/(3*2) = 20 ways to do this
Now assign {1st,2nd,3rd} prizes: 3P3 = 3! = 6 ways PER selection of 3 people.
Multiply 20 selections * 6 arrangements:
20*6 = ways
