SOLUTION: A child forms three-letter "words" using three different letters from HISTORY. A three-letter "word" is any arrangement of three letters, whether it is in the dictionary or not.

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Question 1149142: A child forms three-letter "words" using three different letters from HISTORY. A three-letter "word" is any arrangement of three letters, whether it is in the dictionary or not.
I figured out a-d. I just need help figuring out how to do e.
(e) How many three-letter "words" with exactly one vowel are possible?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52795) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


First case: The vowels are only A-E-I-O-U.

The word HISTORY then contains 2 vowels and 5 other letters. You need to choose 1 of the 2 vowels and 2 of the 5 other letters; and the three letters you choose can be arranged to form a "word" in any of 3! = 6 different ways:

C%282%2C1%29%2AC%285%2C2%29%2A6+=+2%2A10%2A6+=+120

Second case: If you consider Y to be a vowel (as it is in HISTORY), so that the vowels are A-E-I-O-U-Y.

The word HISTORY in this case contains 3 vowels and 4 other letters. Similarly to the analysis above, the number of 3-letter "words" you can form is

C%283%2C1%29%2AC%284%2C2%29%2A6+=+3%2A6%2A6+=+108