JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(A\) be a \(3 \times 3\) matrix having entries from. the set \(\{-1,0,1\}\). The number of all such matrices A having sum of all the entries equal to \(5\) , is
- A \(478\)
- B \(414\)
- C \(456\)
- D \(421\)
Answer & Solution
Correct Answer
(B) \(414\)
Step-by-step Solution
Detailed explanation
Case-I: \(\quad 1 \rightarrow 7\) times and \(-1 \rightarrow 2\) times number of possible matrix \(=\frac{9 !}{7 ! 2 !}=36\) Case-II: \(\quad 1 \rightarrow 6\) times, \(-1 \rightarrow 1\) times and \(0 \rightarrow 2\) times number of possible matrix \(=\frac{9 !}{6 ! 2 !}=252\)…
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