The number of all onto functions from the set $A = {1, 2, 3, \dots n}$ to itself is

n!

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2 n!

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n!^{2}

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n!^{n}

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Solution

The correct option is A $n!$
$A = {1, 2, 3, \dots n}$
Element Number of possible pairing
$1$ $n$
$2$ $n - 1$
$3$ $n - 2$
$\cdot$ $\cdot$
$\cdot$ $\cdot$
$n - 1$ $2$
$n$ $1$
Total number of onto functions
$= n \times n - 1 \times n - 2 \times \dots \times 2 \times 1 = n!$

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Many-One onto Function

Standard XII Mathematics

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The number of all onto functions from the set A={1,2,3,…n} to itself is

The correct option is A n!A={1,2,3,⋯n} Element Number of possible pairing 1 n 2 n−1 3 n−2 ⋅ ⋅ ⋅ ⋅ n−1 2 n 1 Total number of onto functions =n×n−1×n−2×⋯×2×1=n!

The number of all onto functions from the set $A = {1, 2, 3, \dots n}$ to itself is

The correct option is A $n!$
$A = {1, 2, 3, \dots n}$
Element Number of possible pairing
$1$ $n$
$2$ $n - 1$
$3$ $n - 2$
$\cdot$ $\cdot$
$\cdot$ $\cdot$
$n - 1$ $2$
$n$ $1$
Total number of onto functions
$= n \times n - 1 \times n - 2 \times \dots \times 2 \times 1 = n!$