Jevan must paint 3 rooms in a house. Room A can be painted orange, red

Take the task of painting the 3 rooms and break it into stages.

Stage 1: Select a color for Room A
Room A can be painted orange, red or green
So, we can complete stage 1 in 3 ways

Stage 2: Select a color for Room B
Room B can be painted orange, white or red.
So we can complete this stage in 3 ways.

Stage 3: Select a color for Room C
Room C can be painted white, red or green.
So we can complete this stage in 3 ways.

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus paint all 3 rooms) in (3)(3)(3) ways (= 27 ways)

However, some of these 27 possible outcomes BREAK the condition that the 3 rooms cannot all be painted the same color.
Given the different color options for each room, we can see that the ONLY way that the 3 rooms can be the same color is when all 3 rooms are painted RED.
Since there is only 1 way to BREAK the given condition, the number of GOOD outcomes = 27 - 1 = 26

Answer: B

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Let us first properly list out the possible colors for the 3 rooms.

A -> O,R,G
B -> O,W,R
C -> W,R,G

Condition: All 3 rooms cannot be painted with the same color.

The only scenario where all 3 rooms can be painted with the same color is if all the 3 rooms are painted R (Red).

So, every other possibility can be counted except RRR.

How many ways exist to paint the 3 rooms (including RRR too)?


We need to remove RRR from this.

So, the total number of ways for Jevan to paint the house as per the given conditions = 27 - 1 = 26. Choice B.

_____
Harsha

Bunuel: What would be the solution if the question stated: all 03 rooms should have different color?

In this case, I'd simply list all valid combinations where all three rooms are painted different colors.

Room A: Red, Orange, Green
Room B: Red, Orange, White
Room C: Red, Green, White

A - B - C
Red, Orange, Green
Red, Orange, White
Red, White, Green

Orange, Red, Green
Orange, Red, White
Orange, White, Red
Orange, White, Green

Green, Red, White
Green, Orange, Red
Green, Orange, White
Green, White, Red