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Random one-one or onto function: probability it satisfies a given relation

This type of question, asked 2 times: 2021 Paper 23, 28 Jun 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 23

    64
    Let S={1,2,3,4,5,6}S = \{1,2,3,4,5,6\}. Then the probability that a randomly chosen onto function gg from SS to SS satisfies g(3)=2g(1)g(3) = 2g(1) is:

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  2. Question 2

    28 Jun 2022

    167
    The probability that a randomly chosen one-one function from the set {a,b,c,d}\mathbf{\{ a,b,c,d\}} to the set {1,2,3,4,5}\mathbf{\{ 1,2,3,4,5\}} satisfies f(a)+2f(b)−f(c)=f(d)f(a) + 2f(b) - f(c) = f(d) is :

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