Question 1089934
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<pre>
In  {{{C[3]^2}}} . {{{C[10]^5}}} . {{{C[4]^3}}}  ways,


where  {{{C[3]^2}}} is the number of combinations of 3 appetizer taken    2 at a time,   {{{C[3]^2}}} = {{{(3*2)/2}}} = 3;



       {{{C[10]^5}}} is the number of combinations of 10 main courses taken  5 at a time,   {{{C[10]^5}}} = {{{(10*9*8*7*6)/(1*2*3*4*5)}}} = 252;



       {{{C[4]^3}}} is the number of combinations of 4 desserts taken  3 at a time,{{{C[4]^3}}} = {{{(4*3*2)/(1*2*3)}}} = 4.


In all, there are  3 * 252 * 4 = 3024 combinations.
</pre>

Solved.


On combinations, 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>

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>".