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03 Mar 2021, 07:45
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B
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Difficulty:
25%
(medium)
Question Stats:
63% (01:39) correct
37%
(01:51)
wrong
based on 46
sessions
History
Date
Time
Result
Not Attempted Yet
How many arrangements of the letters of the word PARRAMATTA are possible?
A. 18,900
B. 37,800
C. 75,600
D. 151,200
E. 907,200
A. 18,900
B. 37,800
C. 75,600
D. 151,200
E. 907,200
03 Mar 2021, 08:22
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Bunuel
---------------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!)]
-----------------------------
Likewise, we can calculate the number of arrangements of the letters in PARRAMATTA:
There are 10 letters in total
There are 2 identical R's
There are 2 identical T's
There are 4 identical A's
So, the total number of possible arrangements = 10!/[(2!)(2!)(4!)
= 37,800
Answer: B
General Discussion
03 Mar 2021, 11:57
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Arrangment = Total combinations/Common letters combinations.
Here , A-> 4 times
R-> 2 times
T-> 2 times
Therefore, arrangements = 10!/4!*2!*2!
= 37800
Here , A-> 4 times
R-> 2 times
T-> 2 times
Therefore, arrangements = 10!/4!*2!*2!
= 37800
