Algebra and Trigonometry (MindTap Course List) ISBN:9781305071742 Author:James Stewart, Lothar Redlin, Saleem Watson Publisher:Cengage Learning You used combinations rather than permutations; so you are finding the number of sets (order does not matter) of 3 letters including at least one vowel, no repetitions allowed. One of your sets is {A,B,C}. However, the set {A,B,C} is shared by  Each of your and . The result That result can be reached most directly by subtracting the number of 3-consonant no-repeat codes, , from the number of 3-letter no-repeat codes, .
Math Expert Joined: 02 Sep 2009 Posts: 87762
How many 3-letter code words can be formed if at least one of the lett [#permalink]
00:00
Difficulty:
Question Stats: Hide Show timer StatisticsHow 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. 3,380B. 6,615C. 8,315D. 10,140 E. 12,215 _________________
VP Joined: 14 Jul 2010 Status:No dream is too large, no dreamer is too small Posts: 1130
How many 3-letter code words can be formed if at least one of the lett [#permalink]
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. 3,380B. 6,615C. 8,315D. 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 alphabetFor the second position, we can take from the 26 alphabets againFor 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 _________________
VP Joined: 14 Jul 2010 Status:No dream is too large, no dreamer is too small Posts: 1130
Re: How many 3-letter code words can be formed if at least one of the lett [#permalink]
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. 3,380B. 6,615C. 8,315D. 10,140 E. 12,215 I answered A but the OA is C. Would you please help me to learn. I will be obliged. _________________
Manager Joined: 25 Jan 2021 Posts: 103
Re: How many 3-letter code words can be formed if at least one of the lett [#permalink]
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. 3,380B. 6,615C. 8,315D. 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*26Total ways with only consonants= 21*21*21Total ways with atleast 1 Vowel= 26^3-21^3
Re: How many 3-letter code words can be formed if at least one of the lett [#permalink] 28 Jun 2021, 07:03 |
How many 3-letter codewords can be formed if at least one of the letters is to be chosen from the vowels blank 1 exactly two are vowels blank 2 All are consonants blank 3?
zusammenhängende Posts
Urheberrechte © © 2024 frojeostern Inc.
