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.

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(52797) (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200) (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:

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

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