In a stack of cards, 7 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 4/5. What is the number of cards in the stack? Choices:
A) 8  B) 11  C) 12  D) 15  E) 18
This question can be solved by TESTing THE ANSWERS.   We're told that we have 7 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 4/5. We're asked for the TOTAL number of cards.   Normally, when TESTing THE ANSWERS,   Answer A: 8 total cards   With 8 total cards, and 7 blue cards, the probability of pulling two blue cards is...   (7/8)(6/7) = 42/56   Since 4/5 = 0.75, this is clearly the answer.   8
<result>A</result>
In a stack of cards, 7 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 4/5. What is the number of cards in the stack?