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A group of $51$ executives shares $12$ secretaries. Each executive is assigned $1$ secretary and each secretary is assigned to assist at most $5$ executives.

Let $k$ be the number of secretaries who are assigned to $4$ or $5$ executives.

What is the smallest possible value of $k$?

A

$6$

B

$7$

C

$8$

D

$9$

E

$10$

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