In how many ways can cells in a 3 x 3 grid be shaded, such that each row and each column have exactly one shaded cell? A...

Question

In how many ways can cells in a 3 x 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.

A. 2
B. 9
C. 3
D. 6

Accepted Answer

There are 6 ways to shade the 3 x 3 grid satisfying the constraint. Answer: D. Each row must have exactly one shaded cell and each column must have exactly one shaded cell. This means no two shaded cells share a row or column. In a 3 x 3 grid, choosing which column gets the shaded cell in row 1, row 2, and row 3 is exactly the same as counting permutations of the set {1, 2, 3}. The number of such arrangements is 3 factorial = 6.

In how many ways can cells in a 3 x 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown. A. 2 B. 9 C. 3 D. 6