Question 1149142
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First case: The vowels are only A-E-I-O-U.<br>
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:<br>
{{{C(2,1)*C(5,2)*6 = 2*10*6 = 120}}}<br>
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.<br>
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<br>
{{{C(3,1)*C(4,2)*6 = 3*6*6 = 108}}}<br>