Problem Solving

BTGModeratorVI wrote: ↑

Thu Nov 05, 2020 7:58 am

How many ways can the letters in the word COMMON be arranged?

A. 6
B. 30
C. 90
D. 120
E. 180

Answer: E
Source: Official guide

------ASIDE-----------------------
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!)]
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Now on to the question!

The word: COMMON:
There are 6 letters in total
There are 2 identical O's
There are 2 identical M's
So, the total number of possible arrangements = 6!/[(2!)(2!)] = 180

Answer: E

Cheers,
Brent