Carcass wrote:
In how many ways can the letters of the word GARGANTUNG be rearranged such that all the G’s appear together?
(A) \(\frac{8!}{3!*2!*2!}\)
(B) \(\frac{8!}{2!*2!}\)
(C) \(\frac{8!*3!}{2!*2!}\)
(D) \(\frac{8!}{2!*3!}\)
(E) \(\frac{10!}{3!*2!*2!}\)
----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!)]
---------------------------
First,
"GLUE" the 3 G's together to form ONE super letter (which we'll call
X)
So, we must arrange the letters in the word: ARANTUN
XThere are
8 letters in total
There are
2 identical A's
There are
2 identical N's
So, the total number of possible arrangements =
8!/[(
2!)(
2!)]
Answer: B
Cheers,
Brent