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How many -letter "words" can be formed from the standard -letter alphabet, if the first letter must be a vowel (A, E, I, O, or U)? (We aren't necessarily talking about English words; something like EQX is perfectly valid here.)

 Apr 16, 2023
 #1
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How many letter words? It might just be me, but I see your question goes "How many -letter ...".

Do you mean 3-?

Thanks,

 Apr 16, 2023
 #2
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That should say four-letter words.

Guest Apr 17, 2023
 #3
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+5

In that case, we can multiply the number of choices for each letter by each other.

 

We know that the 1st letter has 5 different possible options, A, E, I, O, and U.

 

For the 2nd, 3rd, and 4th letters, there are 26 different possible options for each letter (as there are 26 letters in the alphabet).

 

Now, we can multiply these numbers together.

 

\(5*26*26*26\)

 

If you are lazy like me, you can plug it into a calculator and achieve the result

 

87880.

 

However, if you are a really hardcore mathematician, you can write it out:

 

\( 5*26*26*26 = 130*26*26 = 3380 * 26 = 87880\)

 

Hope this helped!

 

I remain,

BlackjackEd  Apr 17, 2023
 #4
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That answer is wrong.

Guest Apr 17, 2023
 #5
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Hmm, well could you check the question again? (just to be sure)

 

If I am still wrong, my deepest apologies.

BlackjackEd  Apr 17, 2023
 #6
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How many -letter "words" can be formed from the standard -letter alphabet, if the first letter must be a vowel (A, E, I, O, or U)? (We aren't necessarily talking about English words; something like EQX is perfectly valid here.)  

 

Just to toss in my 2¢ worth, I'd say the missing word is three, 

That is, "How many three-letter words...." 

I say this because the example EQX has three letters. 

 

Same reasoning as BlackJack's, the total would be (5 x 26 x 26) = 3,380.   

.

 Apr 17, 2023
 #7
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If the 5 vowels are allowed to repeat, then you should have:

5 x 26^3 ==87,880 - "words"

 

If the vowels are NOT allowed to repeat, then you should have:

5 x 21^3 ==46,305 - "words"

 

Note: The above permutations are for 4-letter "words". For 3-letter "words", there are:

5 x 26^2 ==3,380 - "words"  and  5 x 21^2 ==2,205 - "words"

 Apr 17, 2023

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