SOLUTION: In how many ways can 9 gifts be divided between 4 children if the eldest child is to receive 3 gifts and each of the other children 2 gifts?

Question 1194842: In how many ways can 9 gifts be divided between 4 children if the eldest child is to receive 3 gifts and each of the other children 2 gifts?
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
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In how many ways can 9 gifts be divided between 4 children
if the eldest child is to receive 3 gifts and each of the other children 2 gifts?
~~~~~~~~~~~~~~

There are   =  = 84 choices for the eldest child;

then        = 15 choices for the next (second) child;

            =  6 choices for the next (third) child;

           and finally only one choice without any possible options for the last child.


In all, there are   = 84*15*6 = 7560  different ways to distribute the gifts under given conditions.

Solved.

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This problem is on Combinations and on Fundamental counting principle.

On these subjects, see the lessons

    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
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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