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In how many ways can the word RAINBOW be arranged so that vo
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26 Oct 2019, 04:42
26 Oct 2019, 04:42
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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) \(2880\)
(A) \(144\)
(B) \(512\)
(C) \(720\)
(D) \(1440\)
(E) \(2880\)
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In how many ways can the word RAINBOW be arranged so that vo
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26 Oct 2019, 08:34
26 Oct 2019, 08:34
huda wrote:
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) \(2880\)
(A) \(144\)
(B) \(512\)
(C) \(720\)
(D) \(1440\)
(E) \(2880\)
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
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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Re: In how many ways can the word RAINBOW be arranged so that vo
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24 Oct 2021, 21:43
24 Oct 2021, 21:43
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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