saurabhprashar wrote:
The number of arrangement of letters of the word BANANA in which the two N's do not appear adjacently is:
A. 40
B. 50
C. 60
D. 80
E. 100
---------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!)]
-------ONTO THE QUESTION!!---------------------------------
In BANANA, there are:
There are
6 letters in total
There are
3 identical A's
There are
2 identical N's
So, the total number of possible arrangements =
6!/[(
3!)(
2!)]
=
60IMPORTANT: Among these
60 outcomes, there are some outcomes that break the rule about N's not appearing next to each other.
So, let's determine the number of outcomes in which the 2 N's ARE together, and we'll subtract this from our
60 outcomes.
First "glue" the 2 N's together, to get
one "super letter" NN
So, we now must arrange 5 letters: B, A, A, A, and NN
There are
5 letters in total
There are
3 identical A's
So, the total number of possible arrangements =
5!/(
3!)
=
20Number of arrangements that adhere to the rule =
60 -
20 = 40
Answer: A
Cheers,
Brent
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