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29 Dec 2021, 08:45
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B
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Difficulty:
65%
(hard)
Question Stats:
63% (02:43) correct
38%
(03:08)
wrong
based on 104
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How many words can we make for the PERMUTATIONS word using only one vowel, and 2 consonant that the vowel always been in middle?
A) 154
B) 155
C) 156
D) 157
E) 158
Are You Up For the Challenge: 700 Level Questions
A) 154
B) 155
C) 156
D) 157
E) 158
Are You Up For the Challenge: 700 Level Questions
29 Dec 2021, 23:11
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Let's break PERMUTATIONS into its vowels and consonants -
Vowels - {P,R,M,TT,N,S}
Consonants - {E,U,I,O,A}
So we have six different vowels and 5 different consonants.
Also, we have two consonant which are similar.
Case 1 : The two consonants selected are different
Number of ways of choosing a vowel (middle alphabet of the word) = 5 C 1 = 5
Number of ways of choosing a consonant = 6 P 2 = 30
Total ways = 30 * 5 = 150 ways
Case 2 : The two consonants selected are same
Number of ways of choosing a vowel (middle alphabet of the word) = 5 C 1 = 5
Number of ways of choosing a consonant = 1 (Two Ts)
Total ways = 1 * 5 = 5 ways
Total ways = 150 + 5 = 155 ways
IMO - B
Vowels - {P,R,M,TT,N,S}
Consonants - {E,U,I,O,A}
So we have six different vowels and 5 different consonants.
Also, we have two consonant which are similar.
Case 1 : The two consonants selected are different
Number of ways of choosing a vowel (middle alphabet of the word) = 5 C 1 = 5
Number of ways of choosing a consonant = 6 P 2 = 30
Total ways = 30 * 5 = 150 ways
Case 2 : The two consonants selected are same
Number of ways of choosing a vowel (middle alphabet of the word) = 5 C 1 = 5
Number of ways of choosing a consonant = 1 (Two Ts)
Total ways = 1 * 5 = 5 ways
Total ways = 150 + 5 = 155 ways
IMO - B
gloomybison
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16 Jan 2022, 11:11
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Does "that the vowel always been in middle?" mean anything? I guess it doesn't really matter to solve the question
