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JEE Main 2023 · 24 Jan · Shift 2

JEE Main 2023 Mathematics question on Permutations and Combinations

The number of square matrices of order 5 with entries from the set {0,1}\{0, 1\}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is
  1. A.
    225
  2. B.
    125
  3. C.
    150
  4. D.
    120
Show answer and solution

Correct option: D

Solution

Such matrices are exactly the 5×5 permutation matrices — each row and each column has exactly one 1 and the rest 0s. The number of ways to place the 1s is equivalent to choosing a bijection from {rows} to {columns}, which is 5! = 120.

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