Question 1008174: If a customer purchases a new stereo system during the spring sale, he may choose any 4 CDs from 24 classical and 40 jazz selections. In how many ways can the customer choose 2 of each?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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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