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The number of onto functions from the set $\{1,2, \ldots, 11\}$ to the set $\{1,2, \ldots, 10\}$ is
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The correct answer is:
$10 \times 11 !$
Let $\quad A=\{1,2, \ldots, 11\}$
$\begin{array}{ll}\therefore & n(A)=11 \text { and } B=\{1,2, \ldots, 10\} \\ \therefore & n(B)=10\end{array}$
$\therefore \text{Hence number of onto function}$ $=^{n(A)} C_{n(B)} \times n(B) ! \times n(B)$
$={ }^{11} C_{10} \times 10 ! \times 10$
$=(11 \times 10 !) \times 10=11 ! \times 10$
$\begin{array}{ll}\therefore & n(A)=11 \text { and } B=\{1,2, \ldots, 10\} \\ \therefore & n(B)=10\end{array}$
$\therefore \text{Hence number of onto function}$ $=^{n(A)} C_{n(B)} \times n(B) ! \times n(B)$
$={ }^{11} C_{10} \times 10 ! \times 10$
$=(11 \times 10 !) \times 10=11 ! \times 10$
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