Question 6
A $4 \times 4$ grid made up of $16$ $1 \times 1$ squares is given. Suppose we want to color each of the squares by using one of the four colors, red, blue, yellow or green. How many ways of painting all of the boxes are there if the following requirement must be met:
For any row and any column one of the following 3 conditions must be satisfied:
* all four squares must be colored by the same color.
* use two colors, each one to be used to color two squares.
* use all four colors, each one to be used to color one square.
For any row and any column one of the following 3 conditions must be satisfied:
* all four squares must be colored by the same color.
* use two colors, each one to be used to color two squares.
* use all four colors, each one to be used to color one square.