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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

Respuesta :

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

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