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In how many different ways can the letters of the word MISSISSIPPI be
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13 Oct 2021, 07:06
13 Oct 2021, 07:06
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In how many different ways can the letters of the word MISSISSIPPI be arranged if the vowels must always be together?
A. 48
B. 144
C. 210
D. 420
E. 840
A. 48
B. 144
C. 210
D. 420
E. 840
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Re: In how many different ways can the letters of the word MISSISSIPPI be
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13 Oct 2021, 08:39
13 Oct 2021, 08:39
Carcass wrote:
In how many different ways can the letters of the word MISSISSIPPI be arranged if the vowels must always be together?
A. 48
B. 144
C. 210
D. 420
E. 840
A. 48
B. 144
C. 210
D. 420
E. 840
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!!!-----------------
First "glue" the 4 I's together to create ONE character: IIII (this ensures that they stay together)
So, basically, we must determine the number of arrangements of M, S, S, S, S, P, P and IIII
There are 8 characters in total
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 8!/[(4!)(2!)]
= 840
Answer: E
gmatclubot
Re: In how many different ways can the letters of the word MISSISSIPPI be [#permalink]
13 Oct 2021, 08:39
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