IIT JEE Advanced Combinatorics | 3×3 Symmetric Matrix with 5 1’s and 4 0's | How Many Matrices?

IIT JEE Advanced Combinatorics | 3×3 Symmetric Matrix with Five 1’s and 4 0's | How Many Matrices?

This is an interesting IIT JEE Advanced level problem combining concepts from matrices, symmetry, and combinatorics.

Let A be the set of all 3 × 3 symmetric matrices whose entries are either 0 or 1.
It is given that five entries are 1 and four entries are 0.

Question:
Find the total number of matrices in the set A.

This problem tests your understanding of:

• Properties of symmetric matrices
• Counting techniques in matrices
• Combinatorics in linear algebra

Such questions frequently appear in IIT JEE Advanced, Olympiad mathematics, and other competitive exams.

🎯 Challenge:

Try solving it yourself before watching the solution and see if you can use the symmetry property to reduce the counting!

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📌 Watch till the end to understand the shortcut approach that saves time in the exam.

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