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# How many arrangements are possible with the letters of the

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Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1044
Location: India
GPA: 3.64
How many arrangements are possible with the letters of the  [#permalink]

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03 Jan 2018, 11:19
1
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:42) correct 18% (01:44) wrong based on 63 sessions

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How many arrangements are possible with the letters of the word 'PROFILE', if no two consonants are to come together?

A) 36
B) 120
C) 144
D) 288
E) 576

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Re: How many arrangements are possible with the letters of the  [#permalink]

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03 Jan 2018, 11:29
souvonik2k wrote:
How many arrangements are possible with the letters of the word 'PROFILE', if no two consonants are to come together?

A) 36
B) 120
C) 144
D) 288
E) 576

There are 4 consonants (P, R, F and L) and 3 vowels (O, I and E) in PROFILE. Consider the following: *O*I*E*.

If we place the consonants instead of stars no two consonants will be together. 4 consonants, in places of 4 stars can be arranged in 4! ways and 3 vowels can be arranged in 3! ways, so the total of 4!*3! = 144.

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Re: How many arrangements are possible with the letters of the  [#permalink]

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03 Jan 2018, 19:17
souvonik2k wrote:
How many arrangements are possible with the letters of the word 'PROFILE', if no two consonants are to come together?

A) 36
B) 120
C) 144
D) 288
E) 576

-----------

In 'PROFILE': P,R,F,L are the consonants, the only way they cannot come together is by arranging the vowels (I,E,O) between them i.e. in the blanks aas can be seen below:
P_R_F_L

Lets arrange it:
1. Arrangement of P,R,F,L = 4! ,and
2. Arrangement of blanks which has I,E,O = 3!

Totoal =4!*3!
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Re: How many arrangements are possible with the letters of the  [#permalink]

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03 Jan 2018, 20:12
souvonik2k wrote:
How many arrangements are possible with the letters of the word 'PROFILE', if no two consonants are to come together?

A) 36
B) 120
C) 144
D) 288
E) 576

Here we have 3 vowels (O,I,E) and 4 consonants (P,R,F,L). Since no 2 consonants are to come together, the positions of consonants are * and vowels are _ as following: *_*_*_*.
We have 4! ways to arrange 4 consonants into 4 positions and 3! ways to arrange 3 vowels into 3 positions.
Consequently there are 4!*3!=144 arrangements.
Re: How many arrangements are possible with the letters of the   [#permalink] 03 Jan 2018, 20:12
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