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!)]
-----------------------
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
