Let S={1,2,3,4,5,6} . Then probability that a randomly chosen onto function mathrm{g} from mathrm{S}

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14.Probability

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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

$\frac{1}{30}$

(JEE MAIN-2021)

Solution

$\mathrm{g}(3)=2 \mathrm{~g}(1)$ can be defined in $3$ ways

number of onto functions in this condition $=3 \times 4 !$

Total number of onto functions $=6 !$

Required probability $=\frac{3 \times 4 !}{6 !}=\frac{1}{10}$

Standard 11

Mathematics

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