Question 891173: 12. There are 20 quarts of milk on a supermarket shelf, four of which are spoiled. A customer buys three quarts of milk.
(a) How many samples are possible?
(b) How many samples contain exactly two quarts of spoiled milk?
(c) How many samples contain at least two quarts of spoiled milk?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! There are 20 quarts of milk on a supermarket shelf.
4 of them are spoiled.
That means 16 good and 4 bad.
A customer buys 3 quarts of milk.
Total possible samples that are different from each other is given by the formula of C(20,4) = 20! = 4845
Total possible samples that contain exactly 2 quarts of bad milk are equal to C(4,2) * C(16,1) = 6 * 16 = 96
Total possible samples that contain exactly 3 quarts of bad milk are equal to C(4,3) = 4
Total possible samples that contain at least 2 quarts of bad milk are equal to C(4,2) * C(16,1) + C(4,3) = 96 + 4 = 100
C(n,x) = n! / ((n-x)! * x!)
For Example:
C(4,2) = 4! / (2! * 2!) = 4*3*2*1 / 2*1*2*1 = 6
C(16,1) = 16 * 15! / (1! * 15!) = 16 / 1 = 16.
C(4,3) = 4! / (1!*3!) = 4*3*2*1 / 1*3*2*1 = 4
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