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# In how many ways can the letters of a word 'GMATINSIGHT' be arranged t

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In how many ways can the letters of a word 'GMATINSIGHT' be arranged t  [#permalink]

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24 Feb 2017, 06:41
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:58) correct 22% (00:33) wrong based on 74 sessions

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In how many ways can the letters of a word 'G M A T I N S I G H T' be arranged to form different words (whether the word makes sense or not)?

A) 11!
B) 9!
C) 8!
D) 11!/3!
E) 11!/(2!*2!*2!)

Source: http://www.GMATinsight.com

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Re: In how many ways can the letters of a word 'GMATINSIGHT' be arranged t  [#permalink]

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24 Feb 2017, 07:03
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Top Contributor
GMATinsight wrote:
In how many ways can the letters of a word 'G M A T I N S I G H T' be arranged to form different words (whether the word makes sense or not)?

A) 11!
B) 9!
C) 8!
D) 11!/3!
E) 11!/(2!*2!*2!)

When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]

-----NOW ONTO THE QUESTION-------------------------------------------

Calculate the number of arrangements of the letters in GMATINSIGHT
There are 11 letters in total
There are 2 identical T's
There are 2 identical I's
There are 2 identical G's
So, the total number of possible arrangements = 11!/[(2!)(2!)(2!)]

Cheers,
Brent
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In how many ways can the letters of a word 'GMATINSIGHT' be arranged t  [#permalink]

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24 Feb 2017, 07:27
The permutation of n different things in which a things are alike, another b things are alike, another c things are alike and so on is given by the formula
n!/(a!b!c!...)

We are required to find the numbers of permutations of the letters G M A T I N S I G H T

Total number of letters (n) = 11

There are 2 identical G's. So a=2
There are identical T's. So b=2
There are 2 identical I's. So c=2

There are no other letters which are identical.

So number of different arrangement possible = 11!/(2!2!2!)

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Re: In how many ways can the letters of a word 'GMATINSIGHT' be arranged t  [#permalink]

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28 Nov 2018, 17:49
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Re: In how many ways can the letters of a word 'GMATINSIGHT' be arranged t   [#permalink] 28 Nov 2018, 17:49
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