George has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?	Choose one
A) 2/8
B) 3/15
C) 2/28
D) 3/5
E) 15/28
The probability is equal to the number of desired choices divided by the total number of possibilities.   Probability = Favorable/Total   Total = 8C2 = 8*7/2= 
<gadget id="calculator">8*7/2</gadget>
<output>28</output>
28   Favorable:   Pick 1 sour out of 3 sour   AND   pick 1 sweet out of 5 sweet.   3C1*5C1=3*5= 
<gadget id="calculator">3*5</gadget>
<output>15</output>
15   P=15/28   When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.   Thus,   Total Probability:   Probability of choosing sour candy first AND Probability of choosing sweet candy   OR   Probability of choosing sweet candy first AND Probability of choosing sour candy   Answer: 15/28
<result>E</result>
George has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?