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If a set $A$ has $m$ elements and set $B$ has $n$ elements and the number of injections from $A$ to $B$ is 2520 . Then, $m$ is equal to
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The correct answer is:
5
Given, $|A|=m$ and $|B|=n$
Total number of injective function from $A$ to $B$ is $\frac{n !}{(n-m) !}$
Given, $\frac{n !}{(n-m) !}=2520$
Total number of injections from $A$ to $B={ }^n P_m=2520$
$\begin{array}{ll}
\Rightarrow & { }^n P_m=7 \times 6 \times 5 \times 4 \times 3={ }^7 P_5 \\
\Rightarrow & n=7, m=5
\end{array}$
Total number of injective function from $A$ to $B$ is $\frac{n !}{(n-m) !}$
Given, $\frac{n !}{(n-m) !}=2520$
Total number of injections from $A$ to $B={ }^n P_m=2520$
$\begin{array}{ll}
\Rightarrow & { }^n P_m=7 \times 6 \times 5 \times 4 \times 3={ }^7 P_5 \\
\Rightarrow & n=7, m=5
\end{array}$
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