A mapping is selected at random from the set of all the mappings of the set A = {1, 2, …….., n} into itself. The probability that the mapping selected is an injection is:

\frac{1}{n^{n}}

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\frac{1}{n!}

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\frac{(n - 1)!}{n^{n - 1}}

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\frac{n!}{n^{n - 1}}

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Solution

The correct option is C $\frac{(n - 1)!}{n^{n - 1}}$
Total number of functions (mappings) from $A \to A = n^{n}$
Number of injective (one – one) functions
From $A \to A = n!$
$∴$ Probability = $\frac{n!}{n^{n}} = \frac{(n - 1)!}{n^{n - 1}}$

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A mapping is selected at random from the set of all the mappings of the set A = {1, 2, …….., n} into itself. The probability that the mapping selected is an injection is:

The correct option is C (n−1)!nn−1Total number of functions (mappings) from A→A=nn Number of injective (one – one) functions From A→A=n! ∴ Probability =n!nn=(n−1)!nn−1

The correct option is C $\frac{(n - 1)!}{n^{n - 1}}$
Total number of functions (mappings) from $A \to A = n^{n}$
Number of injective (one – one) functions
From $A \to A = n!$
$∴$ Probability = $\frac{n!}{n^{n}} = \frac{(n - 1)!}{n^{n - 1}}$