document.write( "Question 390475: How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, and E? \n" ); document.write( "

Algebra.Com's Answer #277193 by richard1234(7193) $\"\"$ $\"About$

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The total number of four-letter \"words\" that can be made (duplicating letters if necessary) is 5^4, or 625, since for each position, any of the five letters can appear there.\r
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\n" ); document.write( "\n" ); document.write( "We wish to count the number of four letter \"words\" with no vowels. Then, we can subtract this number from 625 to obtain the number of words with at least one vowel. The number of four letter words with no vowels is 3^4 or 81, since a B, C, or D can appear in any position.\r
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\n" ); document.write( "\n" ); document.write( "Therefore the number of four letter words that satisfy is equal to 5^4 - 3^4, or 544.\r
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\n" ); document.write( "\n" ); document.write( "The case where each letter in the word must be distinct is slightly different. If each letter is distinct, then you are guaranteed to have at least one vowel in the word. Therefore the answer would be 5P4, or 5*4*3*2, or 120. I do not know if the problem asks for distinct letters or not, it could be either 544 or 120 depending on the case. \n" ); document.write( "

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