Question 1194842
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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?
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<pre>
There are  {{{C[9]^3}}} = {{{(9*8*7)/(1*2*3)}}} = 84 choices for the eldest child;

then       {{{C[6]^2}}} = 15 choices for the next (second) child;

           {{{C[4]^2}}} =  6 choices for the next (third) child;

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


In all, there are  {{{C[9]^3*C[6]^2*C[4]^2}}} = 84*15*6 = 7560  different ways to distribute the gifts under given conditions.
</pre>

Solved.


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This problem is on Combinations and on Fundamental counting principle.


On these subjects, see the lessons


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Fundamental-counting-principle-problems.lesson>Fundamental counting principle problems</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



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.