SOLUTION: There are 5 quarters, 2 dimes and 6 pennies in a jar. If you pull three at random what is the probability that you will have three coins with the sum of 36 cents?

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Question 1094336: There are 5 quarters, 2 dimes and 6 pennies in a jar. If you pull three at random what is the probability that you will have three coins with the sum of 36 cents?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

You choosing 3 of the 13 coins in the jar; the number of ways to do that is "13 choose 3":
C%2813%2C3%29+=+286

In order to get a total value of 36 cents, the three coins must be 1 quarter, 1 dime, and 1 penny.

So you need to choose 1 of the 5 quarters ("5 choose 1" = 5 different ways), 1 of the 2 dimes ("2 choose 1" = 2 ways), and 1 of the 6 pennies ("6 choose 1" = 6 ways).

So the total number of ways to get 1 of each coin is
C%285%2C1%29%2AC%282%2C1%29%2AC%286%2C1%29+=+5%2A2%2A6+=+60

Then the probability of getting that desired outcome is the total number of way to get the desired outcome, divided by the total number of ways of picking 3 of the 13 coins:
P+=+60%2F286+=+30%2F143