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The letters of the word PROMISE are arranged so that no two of the vow

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The letters of the word PROMISE are arranged so that no two of the vow  [#permalink]

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New post 26 Nov 2018, 01:01
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A
B
C
D
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Difficulty:

  85% (hard)

Question Stats:

40% (02:46) correct 60% (01:54) wrong based on 43 sessions

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The letters of the word PROMISE are arranged so that no two of the vowels should come together. Find total number of arrangements.

A. 7
B. 49
C. 1.440
D. 1,898
E. 4,320

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Re: The letters of the word PROMISE are arranged so that no two of the vow  [#permalink]

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New post 26 Nov 2018, 04:25
1
Really Good Question

i learned it the hard way , hope my solution helps

__C__C__C__C__
Here is the arrangement of 4 Consonant such that between any two Consonant at most one Vowel can come but since the Vowels can also appear before the leftmost Consonant or after the rightmost Consonant so it gives us 5 places available for Vowels(represented by “___”)

But since we require only 3 places due to 3 vowels to be arranged so we will select the 3 places out of 5 in 5C3 ways = 10 ways

In the given arrangement the Consonants can be arranged in 4! Ways at the selected 4 places and,

All the vowels can also be arranged among themselves in 3! Ways

so Total ways to arrange the letters as per desired condition = 10*3!*4! = 1440

Answer: Option C


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Re: The letters of the word PROMISE are arranged so that no two of the vow  [#permalink]

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New post 26 Nov 2018, 12:41
This can also be solve as an overlapping set problem -
7!(total arrangements without restrictions) - 3.2.6!(arrangements when any 2 of three are together) + 5!.6 (removing one duplicate overlapping of all three together from previous as this will happen twice) = 1440.

Ans C.
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Re: The letters of the word PROMISE are arranged so that no two of the vow  [#permalink]

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New post 26 Nov 2018, 17:18
Bunuel wrote:
The letters of the word PROMISE are arranged so that no two of the vowels should come together. Find total number of arrangements.

A. 7
B. 49
C. 1.440
D. 1,898
E. 4,320



Combine vowels together so we are left with 4 places for Consonants and 1 for vowels out of 7 we will have now 4+1 = 5 ways and since 3 vowels are given then the combination to arrange this array is 5c3
Now since no 2 vowels are to be together , so no. of ways to arrange C in 4 places 4 ! and vowels 3! = total arrangements hence possible = 5c3*4!*3! = 1440 option C
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Re: The letters of the word PROMISE are arranged so that no two of the vow &nbs [#permalink] 26 Nov 2018, 17:18
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The letters of the word PROMISE are arranged so that no two of the vow

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