Bunuel
A garden shed contains a total of 8 bags of yard care supplies. There are 3 bags of fertilizer and 2 bags of grass seed, and the remaining bags are of mulch. If 3 bags are selected from the shed at random, one at a time without replacement, what is the probability that none of the bags are of mulch?
A. 1/56
B. 15/128
C. 5/28
D. 125/336
E. 3/8
Solution:The probability that no bags are mulch is:
(5C3) / (8C3)
5C3 = (5 x 4 x 3) / 3! = 5 x 2 = 10
8C3 = (8 x 7 x 6) / 3! = 8 x 7 = 56
Thus, the overall probability is 10/56 = 5/28.
Alternate Solution:The probability of choosing the first bag that’s not mulch is 5/8. Because we are drawing without replacement, the probability that the second bag is not mulch is 4/7. The probability that the third bag drawn is not mulch is 3/6. Thus, the probability that we choose 3 bags, none of which is mulch, is
5/8 x 4/7 x 3/6 = 60/336 = 10/56 = 5/28.
Answer: C