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I have a matrix of order 5 x 5

I would like to replace the

2 elements in column 1 with 0's

1 elements in column 2 with 0's

4 elements in column 3 with 0's

3 elements in column 4 with 0's

2 elements in column 5 with 0's

What are the different number of matrices available if I do replace.

Hoe can this be solved for a general case if matrix is of m x n