Question 1168327: 8C4/12C4 perform the indicated calculationn
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you have a calculator that does this for you, you will get.....
8C4 = 70
12C4 = 495
8C4 / 12C4 = 70/495
this simplifies to 14/99.
if you don't have a calculator that does this for you, then you have to do it by formula.
the combination formula is nCx = n! / (x! * (n-x)!)
you get:
8C4 = 8! / (4! * 4!)
this is the same as:
8C4 = (8 * 7 * 6 * 5 * 4!) / (4! * 4!)
the 4! in the numerator and denominator cancel out and you are left with:
8C4 = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
solve for 8C4 to get:
8C4 = 70
and you get:
12C4 = 12! / (4! * 8!)
this is the same as:
12C4 = (12 * 11 * 10 * 9 * 8!) / (4! * 8!)
the 8! in the numerator and denominator cancel out and you are left with:
12C4 = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
solve for 12C4 to get:
12C4 = 495
8C4 / 12C4 = 70 / 495 = 14 / 99, same as before.
in decimal format, it is equal to .141414......
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