Problem Solving

Max@Math Revolution wrote:[GMAT math practice question]

How many possible 7-digit codes can be formed from the letters s, u, c, c, e, s, s?

A. 400
B. 420
C. 450
D. 500
E. 510

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 ONTO THE QUESTION--------------------

In the word SUCCESS,
There are 7 letters in total
There are 2 identical C's
There are 3 identical S's
So, the total number of possible arrangements = 7!/[(2!)(3!)]
= 420

Answer: B

Cheers,
Brent