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Number of onto (or not onto) functions between finite sets

This type of question, asked 4 times: 6 Apr 2023, 8 Apr 2023, 23 Jan 2026 S2, 4 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    6 Apr 2023

    83
    The number of ways of giving 20 distinct oranges to 3 children such that each child gets at-least one orange is

  2. Question 2

    8 Apr 2023

    179
    Let R={a,b,c,d,e}\mathbf{R = \{ a,b,c,d,e\}} and S={1,2,3,4}\mathbf{S = \{ 1,2,3,4\}}. Total number of onto function f:R→Sf:R \rightarrow S such that f(a)≠f(a) \neq 1 , is equal to

  3. Question 3

    23 Jan 2026 S2

    55
    Consider two sets A={x∈Z:∣∣x−3∣−3∣≤1}A=\{x\in Z:||x-3|-3|\le 1\} and B={x∈R−{1,2}:(x−2)(x−4)x−1log⁡e(∣x−2∣)=0}B=\left\{x\in R-\{1,2\}:\frac{(x-2)(x-4)}{x-1}\log_{e}(|x-2|)=0\right\}. Then the number of onto functions f:A→Bf:A\rightarrow B is equal to:

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  4. Question 4

    4 Apr 2026 S1

    54
    The number of functions f:{1,2,3,4}→{a,b,c}\mathbf{f:\{ 1,2,3,4\} \rightarrow \{ a,b,c\}}, which are not onto, is :

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