JEE MAIN - Mathematics (2021 - 31st August Evening Shift - No. 3)
Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :
$${1 \over {10}}$$
$${1 \over {15}}$$
$${1 \over {5}}$$
$${1 \over {30}}$$
Explanation
g(3) = 2g(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 = $${{3 \times 4!} \over {6!}} = {1 \over {10}}$$
number of onto functions in this condition = 3 $$\times$$ 4!
Total number of onto functions = 6!
Required probability = $${{3 \times 4!} \over {6!}} = {1 \over {10}}$$
Comments (0)
