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 need help with this counting problem
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raghu
Senior Member

USA
37 Posts

Posted - 08/30/2010 :  12:24:04  Show Profile  Reply with Quote
On the refrigerator, MATHCOUNTS is spelled out with 10 magnets. one letter per magnet. Two vowels and three consonents fall off and are put away. If the Ts are indistinquishable, how many distinct possible collections of letters could be in the bag?
I started out as follows:
5c1 + 5c2+5c3 + 5c4+5c5.
But the answer is 75.
Can someone help me please?
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someguy
Advanced Member

Canada
143 Posts

Posted - 09/02/2010 :  11:57:41  Show Profile  Reply with Quote
Look at the three consonents first.

How many distinguishalbe ways can you end up with 0 T's if order does not matter?
How many distinguishalbe ways can you end up with 1 T if order does not matter?
How many distinguishalbe ways can you end up with 2 T's if order does not matter?

How many distinguishable ways can you select your three consonents if order does not matter? (10 + 10 + 5)

Now look at the vowels.

How many ways can you select two vowels if the order does not matter? (3)

Can you finish it from here?


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someguy
Advanced Member

Canada
143 Posts

Posted - 09/02/2010 :  12:01:52  Show Profile  Reply with Quote
You could also answer the question of

"How many distinguishable ways can you select your three consonants if order does not matter?"

by asking how many ways can you choose 3 consonants from a set of 7 and then figuring out how many times you have counted things you care about more than once.
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raghu
Senior Member

USA
37 Posts

Posted - 09/02/2010 :  12:10:58  Show Profile  Reply with Quote
Thank you Mr. Someguy!
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