AAPL wrote: ↑Sat May 16, 2020 9:43 am
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
