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?
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)
"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.
Interactive Math Goodies Software
need help with this counting problem
Posted - 08/30/2010 : 12:24:04
