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A \(2 \times 2\) matrix is filled with four distinct integers randomly chosen from the set \(\{1,2,3,4,5,6\}\). Then the probability that the matrix generated in such a way is singular is

Question and options

A 2×22 \times 2 matrix is filled with four distinct integers randomly chosen from the set {1,2,3,4,5,6}\{1,2,3,4,5,6\}. Then the probability that the matrix generated in such a way is singular is
  1. 245\frac{2}{45}
  2. 145\frac{1}{45}
  3. 415\frac{4}{15}
  4. 115\frac{1}{15}

Answer and explanation

Correct answer: A - \(\frac{2}{45}\)
Ordered fillings: 6*5*4*3=360. Singular needs ad=bc with four distinct numbers: only 1*6=2*3 and 2*6=3*4. Each gives 2 (which pair on diagonal)*2*2 orderings=8, total 16. P=16/360=2/45.

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