SOLUTION: 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

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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