Color cars

[showbu]

Q31:
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: Spoiler Code A

[sonu_thekool]

The answer is 20 (A)

Here's how. If you are aware, there is an anagram approach. To arrange the words PAPA in all different forms - you can come up with all arrangements by dividing the total number of items divided by the factorial corresponding to the sets of indistinguishable items.

So, PAPA (2 sets of indistinguishable items) can be arranged in 4! / (2! * 2!) = 12/2 = 6

Similarly here, you have RRRBY = which can be arranged in 5! / 3! = 20.

Hope this helps. What is the OA ?