Question 1061363
.
The student association each year selects a council consisting of seven members. 
if there are 10 candidates for the seven member council, how many different councils may be elected?
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{{{C[10]^7}}} = {{{10!/(3!*7!)}}} = {{{(10*9*8)/(1*2*3)}}} = 10*3*2 = 60.


<U>Answer</U>. There are 60 ways to do it.


The symbol {{{C[10]^7}}} is the number of combinations of 10 things taken 7 at a time.



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, 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 "<U>Combinatorics: Combinations and permutations</U>".