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The number of injective functions from a set $X$ containing m elements to a set $Y$ containing $n$ elements for $m > n$ is:

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^{m} P_{n}

(m - n)!

^{m} C_{n}

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detailed solution

Correct option is D

function from $X$ to $Y$ then $n \geq$ where $n = n (X)$ and $n = n (Y)$ The number of injective functions from $X$ to $Y$ is

$n (n - 1) (n - 2) \dots (n - m + 1) =^{n} P_{m}$

As $m > n$ , there does not exist any injective function from $x$ to $y$

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The number of injective functions from a set X containing m elements to a set Y containing n elements for m>n is: