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 Statistics
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
_________________
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
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