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hudacse6
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In how many ways the word RAINBOW can be arranged so that vowel always Updated on: 27 Oct 2019, 08:53
Originally posted by hudacse6 on 25 Oct 2019, 04:30.
Last edited by Bunuel on 27 Oct 2019, 08:53, edited 3 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

72% (01:14) correct 28% (01:34) wrong based on 53 sessions

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In how many ways can the word RAINBOW be arranged so that vowels always come before the consonants?

A. 144
B. 512
C. 720
D. 1440
E. 2880
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A
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Mohammadmo
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In how many ways the word RAINBOW can be arranged so that vowel always 25 Oct 2019, 04:37
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3!×4!=6×24=144

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hudacse6
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In how many ways the word RAINBOW can be arranged so that vowel always 25 Oct 2019, 04:41
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Mohammadmo
3!×4!=6×24=144

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read the question carefully. Mohammadmo
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In how many ways the word RAINBOW can be arranged so that vowel always 25 Oct 2019, 11:30
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Need a better way explanation
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BrentGMATPrepNow
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In how many ways the word RAINBOW can be arranged so that vowel always 26 Oct 2019, 09:38
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hudacse6
In how many ways can the word RAINBOW be arranged so that vowels always come before the consonants?

A. 144
B. 512
C. 720
D. 1440
E. 2880
Show more

Take the task of arranging the letters and break it into stages.

Stage 1: Arrange the 3 vowels (A, I and O) in a row
Property: We can arrange n different objects in n! ways.
So, we can arrange the 3 vowels in 3! ways (= 6 ways)
So, we can complete stage 1 in 6 ways

Stage 2: Arrange the 4 consonants (R, N, B, and W) in a row
So, we can arrange the 4 consonants in 4! ways (= 24 ways)
So, we can complete stage 2 in 24 ways

Stage 3: Place the arrangement of vowels before the arrangement of consonants
We can complete this stage in 1 ways

We're now done arranging all of the letters.

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus arrange the 7 letters) in (6)(24)(1) ways (= 144 ways)

Answer: A
I'm pretty sure the OA is incorrect.


Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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