JEE Mains · Maths · STD 11 - 6. permutation and combination
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
- A \(225\)
- B \(120\)
- C \(150\)
- D \(125\)
Answer & Solution
Correct Answer
(B) \(120\)
Step-by-step Solution
Detailed explanation
In each row and each column exactly one is to be placed - \(\therefore\) No. of such materials \(=5 \times 4 \times 3 \times 2 \times 1=120\) Step\(-1:\) Select any \(1\) place for \(1\) 's in row \(1\). Automatically some column will get filled with 0 's. Step\(-2:\) From next…
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