There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5...

[AAPL]

Official Guide

There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

A. 20
B. 25
C. 40
D. 60
E. 125

OA A

[Brent@GMATPrepNow]

Official Guide

There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

A. 20
B. 25
C. 40
D. 60
E. 125

OA A

Let R, R, R, B, Y represent the cars (by their colors)
Notice that the three R's are identical.
So, the question becomes In how many different ways can we arrange the letters R, R, R, B and Y?

----------------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!------------------------------

We have R, R, R, B and Y:
There are 5 letters in total
There are 3 identical R's
So, the total number of possible arrangements = 5!/(3!)
= (5)(4)(3)(2)(1)/(3)(2)(1)
= 20

Answer: A

Cheers,
Brent

[ygcrowanhand]

This is a classic case of Mississippi Rule:

What you need to do is find the total number of cars: 5

Then divide by the factorial of the repeated terms: 2

So in this case, it's 5!/2! = 20

There's a video version of the question here: https://youtube.com/shorts/wiqRKGpvHMo?feature=share