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If you have 7 different colors of paint and you want to paint a 4\times4 grid such that each row and column must contain all 7 colors, how many different ways can you paint the grid?

Option: 1

15,120


Option: 2

11,880


Option: 3

18,660


Option: 4

16,240


Answers (1)

best_answer

To determine the number of different ways to paint a 4x4 grid using 7 different colors of paint, such that each row and column contains all 7 colors, we can use the concept of permutations.

First, let's consider the first row of the grid. We have 7 options for the first cell, 6 options for the second cell (since it must be a different color from the first cell), 5 options for the third cell (different from the first two cells), and 4 options for the fourth cell (different from the previous three cells).

The number of ways to paint the first row is:

7 (options for the first cell) \times 6 (options for the second cell) \times 5 (options for the third cell) \times4 (options for the fourth cell) = 840

Now, for the second row, we have 3 remaining colors to choose from (since we have already used 4 colors in the first row). Similarly, we have 3 options for the third row and 2 options for the fourth row.

The number of ways to paint the entire grid is:

840 (ways to paint the first row) \times3 (options for the second row) \times 3 (options for the third row) \times 2 (options for the fourth row) = 15,120

Therefore, there are 15,120 different ways to paint a 4x4 grid using 7 different colors of paint, such that each row and column contains all 7 colors.

 

Posted by

Gautam harsolia

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