Posted by Zoe on Saturday, February 21, 2009 at 9:08pm.
Three coins are selected from 10 coins: 4 dimes, 4 nickels, and 2 quarters.
In how many possible ways can the selection be made so that the value of the coins is at least 25 cents?
I know that the total outcomes equals 120, but how do I find how many of these have the value of at least 25 cents?

math  Zoe, Saturday, February 21, 2009 at 10:35pm
The answer is 92. Anyone have idea how to solve this or why the answer is 92? Thanks in advance!

math  Reiny, Sunday, February 22, 2009 at 10:20am
Consider the cases which do not add up to 25, they would be
DNN and NNN
DNN  C(4,1)C(4,2) = 24
NNN  C(4,3 = 4
so 28 cases are not allowed
leaving 120  28 = 92
another way:
You have to list the possible outcomes , then evaluate each one, finally add up the allowable cases
QQQ  C(4,1) = 4
QQD  C(2,2)C(4,1) = 4
QNN  C(2,1)C(4,2) = 12
QDD  .... = 12
QND  .... = 32
DDD  .... = 4
DDN  .... = 24
DNN gives us < 25 cents
NNN gives us < 25 cents.
the total of the above is 92
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