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!)]
Answer: E
Cheers,
Brent
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