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How many 3-letter code words can be formed if at least one of the lett

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Bunuel
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How many 3-letter code words can be formed if at least one of the lett [#permalink] New post   03 Jan 2021, 13:50
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How many 3-letter code words can be formed from the letters of the English alphabet, if at least one of the letters is to be chosen from the vowels a, e, i, o, and u?

A. 3,380
B. 6,615
C. 8,315
D. 10,140
E. 12,215
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ShaikhMoice
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Re: How many 3-letter code words can be formed if at least one of the lett [#permalink] New post   28 Jun 2021, 08:03
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MHIKER wrote:
Bunuel wrote:
How many 3-letter code words can be formed from the letters of the English alphabet, if at least one of the letters is to be chosen from the vowels a, e, i, o, and u?

A. 3,380
B. 6,615
C. 8,315
D. 10,140
E. 12,215


I answered A but the OA is C. Would you please help me to learn. I will be obliged.



Total ways without restriction= 26*26*26
Total ways with only consonants= 21*21*21
Total ways with atleast 1 Vowel= 26^3-21^3
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How many 3-letter code words can be formed if at least one of the lett [#permalink] New post   03 Jan 2021, 14:28
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Bunuel wrote:
How many 3-letter code words can be formed from the letters of the English alphabet, if at least one of the letters is to be chosen from the vowels a, e, i, o, and u?

A. 3,380
B. 6,615
C. 8,315
D. 10,140
E. 12,215


The problem didn't tell us that we can't repeat. And we have to confirm at least one vowel, so we have more than one vowel too.

For the first position, we can take one from the 26 alphabet

For the second position, we can take from the 26 alphabets again

For the third position, we will confirm the vowel from the 5, because if we don't get any vowel in the first try. We don't need to maintain any order.

Thus the ways: \(26*26*5=3,380\)

The answer is A
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Re: How many 3-letter code words can be formed if at least one of the lett [#permalink] New post   10 Jan 2021, 08:46
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Bunuel wrote:
How many 3-letter code words can be formed from the letters of the English alphabet, if at least one of the letters is to be chosen from the vowels a, e, i, o, and u?

A. 3,380
B. 6,615
C. 8,315
D. 10,140
E. 12,215


I answered A but the OA is C. Would you please help me to learn. I will be obliged.
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MM2008
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How many 3-letter code words can be formed if at least one of the lett [#permalink] New post   07 Jan 2024, 07:06
Why do we not get the same result if we do (21*21*5) + (21*5*5) + (5*5*5)
i.e., (2 consonants and 1 vowel OR 1 consonant and 2 vowels OR 3 vowels)?
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Re: How many 3-letter code words can be formed if at least one of the lett [#permalink] New post   07 Jan 2024, 08:36
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MM2008 wrote:
Why do we not get the same result if we do (21*21*5) + (21*5*5) + (5*5*5)
i.e., (2 consonants and 1 vowel OR 1 consonant and 2 vowels OR 3 vowels)?


That approach does not account for the different permutations of the first two cases, so it should be 3*(21*21*5) + 3*(21*5*5) + (5*5*5)
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Re: How many 3-letter code words can be formed if at least one of the lett [#permalink]
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