GATE CE 2023 Set 2 — Question 3
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
In how many ways can cells in a grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.
Correct answer
(D) 6
Solution
This problem asks for the number of ways to place 3 shaded cells such that no two are in the same row or column. This is equivalent to finding the number of permutation matrices.
1.For the first row, there are 3 possible columns to choose for the shaded cell.
2.For the second row, the shaded cell cannot be in the same column as the first row's cell, leaving 2 possible columns.
3.For the third row, only 1 column remains available.
Total number of ways = .Continue learning with Success Tracker
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