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13 Jan 2022, 07:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (01:38) correct
40%
(01:50)
wrong
based on 237
sessions
History
Date
Time
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How many different words can be formed with the letters of the word EQUATION without changing the relative order of the vowels and consonants?
A. 125
B. 620
C. 720
D. 880
E. None of these
A. 125
B. 620
C. 720
D. 880
E. None of these
18 Jan 2022, 08:32
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I don't know what it means to not "change the relative order of the vowels and consonants" -- does it mean we're not changing the order of vowels and consonants relative to each other? Or does it mean we're not changing the order of the vowels relative to the other vowels, and of the consonants relative to the other consonants? As the question is written, I think the answer has to be 'one', because if we can't change the 'relative order' of any of the vowels or consonants in 'EQUATION', there's nothing we can change. To make a new word, we need to change the order of some of the letters, and that changes the 'relative order' of some of the vowels and consonants, i.e. of the letters in the word.
I could imagine the question might mean to ask one of two things: either we leave consonants in the 2nd, 5th and 8th positions (but can mix them up) and vowels in the other positions (and can mix them up). Then we can scramble the vowels in 3! ways, the consonants in 5! ways, and thus all of the letters in 3! * 5! = 720 ways.
But the question could also mean that the vowels need to remain in the order E, U, A, I, O in any word we make, and the consonants need to remain in the order Q, T, N in any word we make, so words like QTNEUAIO or EQUAITN or EUAIOQTN would be valid words. Then we're just choosing three of the eight positions in the word that will become our vowels, and that will determine the word completely, and the answer is 8C3 = 56.
When "none of these" is an answer choice, I can't even tell from the answer choices which meaning is intended, but I'm guessing it's the first meaning, with the answer 720.
I could imagine the question might mean to ask one of two things: either we leave consonants in the 2nd, 5th and 8th positions (but can mix them up) and vowels in the other positions (and can mix them up). Then we can scramble the vowels in 3! ways, the consonants in 5! ways, and thus all of the letters in 3! * 5! = 720 ways.
But the question could also mean that the vowels need to remain in the order E, U, A, I, O in any word we make, and the consonants need to remain in the order Q, T, N in any word we make, so words like QTNEUAIO or EQUAITN or EUAIOQTN would be valid words. Then we're just choosing three of the eight positions in the word that will become our vowels, and that will determine the word completely, and the answer is 8C3 = 56.
When "none of these" is an answer choice, I can't even tell from the answer choices which meaning is intended, but I'm guessing it's the first meaning, with the answer 720.
