CombinatoricsProbability(Ron,Stacey help pz)

[Capthan]

Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.

Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?


8/33

62/165

17/33

103/165

25/33

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In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
5/21
3/7
4/7
5/7
16/21
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Can you help me with one method that works for both questions. It seems to me that these questions are not very different from each other. The explanations and methods of solving them are somehow different in M-GMAT prep.

[TLC]

Has anyone answered the questions Capthan posted? I would also like to get a better explanation of the Friends problem. Thanks-

[ahistegt]

Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.

Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?


8/33

62/165

17/33

103/165

25/33

I would appreciate if someone could try to solve it using counting method.

[JonathanSchneider]

I'll give you some tips to get started, but I'd like you to flesh out your own thoughts on the matter here in another post.

For the first question, notice the words "at least." This is indicative that we may want to use the "1 - x" trick.

For the second question, first create a small drawing showing the people and the ways that these friendships break down. You should soon see that there has to be a certain set-up for how the friendships break down. From there, start with the anagram method...

[Capthan]

Jonathan,
I know how to solve these questions. My question is if there is one single and simple method that can be applied to both questions equally.

[ahistegt]

In the link below you can find a good explanation to solve the first one using, among others, counting method:
http://www.manhattangmat.com/forums/post6500.html

[ahistegt]

In the link below you can find a good explanation to solve the second one using, among others, counting method:
http://www.manhattangmat.com/forums/post1439.html

[JonathanSchneider]

Thanks for that! : )