Question

For a positive integer $n,$ the factorial notation $n!$ represents the product of the integers from $n$ to $1.$ For example:

$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$

What value of $N$ satisfies the following equation?

$5! \times 9! = 12 \times N!$

$10$

$11$

$12$

$13$

$14$

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Because $5!=120=12\cdot10,$ the equation becomes $12\cdot10\cdot9!=12\cdot N!.$ Canceling $12$ gives $N!=10\cdot9!=10!,$ so $N=10.$

Thus, the correct answer is A.