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?

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(52798) (Show Source): You can put this solution on YOUR website!
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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.

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On combinations, read the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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