There are 3 available colors and 4 houses. In how many

Question

There are 3 available colors and 4 houses. In how many different ways can the 4 houses be painted if each house can get only one color?

chets · Answer

If each house can get only one color, then they can be painted in 3^4 ways or 81.

MBAlad · Answer

Does it mean that only 3 houses can have colours and the fourth remains unpainted?

If only 3 houses can be painted then number of ways 3 houses can be chosen from 4 = 4C3 = 4

Number of ways 3 houses can be painted using 3 colours = 3! = 6

Total number of possibilities = 4*6 = 24?????????

conocieur · Answer

i'm confused why isn't 4^3?

anindyat · Answer

3^4 
Because each house can be painted in 3 ways. Therefore, total number of possible cases for 4 houses = 3 * 3 * 3 * 3

mst · Answer

The first house can be painted in 3 colors. For every 3 colors of the first house, the second house can also have possible 3 colors...and so on. So, 3x3x3x3 = 81

Just consider the simple example in the attached document. where 2 houses can be painted in 3 colors, and you get 9 possible combinations: 3x3

conocieur · Answer

very clear, thank you guys

There are 3 available colors and 4 houses. In how many

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