JEE Mains · Maths · STD 11 - 14. probability
Let \(S=\{1,2,3,4,5,6\} .\) Then the probability that a randomly chosen onto function \(\mathrm{g}\) from \(\mathrm{S}\) to \(\mathrm{S}\) satisfies \(g(3)=2 g(1)\) is :
- A \(\frac{1}{10}\)
- B \(\frac{1}{15}\)
- C \(\frac{1}{5}\)
- D \(\frac{1}{30}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{10}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{g}(3)=2 \mathrm{~g}(1)\) can be defined in \(3\) ways number of onto functions in this condition \(=3 \times 4 !\) Total number of onto functions \(=6 !\) Required probability \(=\frac{3 \times 4 !}{6 !}=\frac{1}{10}\)
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