<PRE><B>Question 1008174</B>
24c2 * 40c2 = 215280


ncx is the combination formula of extracting x out of n where order is not important.


ncx = n! / (x! * (n-x)!)


24c2 = 24! / (2! * 22!) = (24*23*22!) / (2!*22!) = (24*23)/2! = 12*23 = 276


40c2 = 40! / (2! * 38!) = (40*39*38!) / (2! * 38!) = (40*39)/2! = 20*39 = 780


276 * 780 = 215280.


if you want to see how this works, use much smaller numbers.


assume 3 of each.


you get 3c2 * 3c2 = 3*3 = 9


let abc be the 3 possible selections of classical.
let 123 be the 3 possible selections of jazz.


3c2 of abc = ab, ac, bc
3c2 of 123 = 12, 13, 23


3c2 * 3c2 = 9 becomes:


ab12
ab13
ab23

ac12
ac13
ac23

bc12
bc13
bc23


the same concept works with the much larger numbers.




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