If $B = {1, 2, 3}$ and $A = {4, 5, 6, 7, 8}$ , then the number of surjections from $A$ to $B$ is

81

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64

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48

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150

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Solution

The correct option is D $150$
Number of surjections from A to B
$= 3^{5} -^{3} C_{2} (2^{5} - 2) - 3$
$= 243 - 3 (30) - 3$
$= 150$

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