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For a sports meet, a winners' stand comprising three wooden blocks is in the following form :  There are six different colours available to choose from and each of the three wooden blocks is to be painted such that no two of them has the same colour. In how many different ways can the winners' stand be painted? 

For a sports meet, a winners' stand comprising three wooden blocks is in the following form :  There are six different colours available to choose from and each of the three wooden blocks is to be painted such that no two of them has the same colour. In how many different ways can the winners' stand be painted?  Correct Answer 120

Given:

There are 6 colours and three winner blocks.

Calculation:

Three colours have to be chosen from the six colours so that the colours won't repeat.

This will be solved using the permutation method.

Number of colors = n = 6

Number of colors to be chosen = r = 3

nPr = n! / ( n - r )!

⇒ 6! / ( 6 - 3 )!

⇒ (6 × 5 × 4 × 3 × 2 × 1)/(3 × 2 × 1)

⇒ 6 × 5 × 4

⇒ 120

∴ There are 120 different ways to paint the winner blocks with no two blocks having the same colour.

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