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

Question 320496: A child forms three-letter words using three different letters from HISTORY. A three letter word is any arrangement of three letters, whether in dictionary or not.
There are three segments of the answer that I cannot find the answer to. I need to know how many three-letter words beginning with H are possible, how many begin with a vowel and how many have a vowel as the middle letter.
My answers are:
beginning with an H= 1*6*6=36
beginning with a vowel= 3*7*7=147
with a vowel as the middle letter= 7*3*7=147
The back of the book gives the answers 30, 60, and 60. What am I doing wrong?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
with an "H" in the 1st position , 6 letters remain for the 2nd position , and then 5 remain for the 3rd
___ 6 * 5 = 30

they don't seem to consider "Y" a vowel
___ starting with "I" or "O" in 1st the first position , 6 letters remain for 2nd , and 5 letters remain for 3rd
___ 2 * 6 * 5 = 60

the position of the vowel doesn't change the numerical outcome
___ a vowel in the 2nd position , 6 letters for the 1st position , and 5 letters for the 3rd position
___ 6 * 2 * 5 = 60

hope this helps
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