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QJEEM23Maacfb: JEE Main 2023 Mathematics - Class 11 JEEM23Maacfb Solution: The number of square matrices of order 5 with entries from the…

The number of square matrices of order 5 with entries from the set {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 :

Multiple Choice Options

  • A 125
  • B 150
  • C 225
  • D 120

Step-by-Step Verified Solution

JEE Main 2023 (Online) 24th January Evening Shift Mathematics - Permutations and Combinations Question 58 English Explanation

∵\because In every row and every column there would be exactly one 1 and four zeroes.

Number of matrices =5C1⋅4C1⋅3C1⋅2C1⋅1C1=={ }^{5} C_{1} \cdot{ }^{4} C_{1} \cdot{ }^{3} C_{1} \cdot{ }^{2} C_{1} \cdot{ }^{1} C_{1}= 120

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