A square is bisected vertically and horizontally into 4 smaller squares, and each of the 4 smaller squares is to be painted so that adjacent squares have dif - ferent colors. if there are 20 paints available, in how many ways can the 4 smaller squares be painted

Question

Roach

Mathematics

29 October, 09:11

A square is bisected vertically and horizontally into 4 smaller squares, and each of the 4 smaller squares is to be painted so that adjacent squares have dif - ferent colors. if there are 20 paints available, in how many ways can the 4 smaller squares be painted

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Answers (1)

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Joslyn Nelson · Answer 1

If we just take 4 of the paints there are 4! = 24 ways of painting the 4 squares.

We need to multiply this by 20C4 - the number of combinations of 4 from 20.

20C4 = (20*19*18*17) / (4*3*2*1) = 4845

so the answer is 24 * 4845 = 116,280