First slide

Permutations

Question

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

Moderate

A

$^{m} P_{n}$
B

$(m - n)!$
C

$^{m} C_{n}$
D

0

Solution

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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