Question 1197366
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<pre>

    P = {{{C[7]^3/C[8]^4}}} = {{{35/70}}} = {{{1/2}}} = 0.5 = 50%.    <U>ANSWER</U>
</pre>

The denominator is the number of all different possible quadruples of 8.


The numerator is the number of all such quadruples containing James.


Solved and explained.



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This problem assumes that you are familiar with &nbsp;COMBINATIONS - - - this knowledge is a pre-requisite.


On &nbsp;Combinations, &nbsp;see introductory 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>". 



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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Sometimes, when I explain such solutions to students, I calculate the number of combinations manually,

using and showing explicit formulas.


But had I do it this way every time, &nbsp;I, &nbsp;probably, &nbsp;would lose my mind.


Therefore, &nbsp;often &nbsp;I &nbsp;use &nbsp;MS &nbsp;Excel software in my computer writing


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=combin(N,n), &nbsp;when &nbsp;I &nbsp;need the value  &nbsp;&nbsp;{{{C[N]^n}}}.