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The expression n! is defined as the product of the integers from 1 through n . If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to \frac{p}{q} ?

Explanation	Calculations	Help
$Express p as a ratio of factorials by observing that multiplying the integers from 100 through 299 is equivalent to dividing 299! by the product of integers from 1 through 99.$	$p = \frac{299 !}{99 !}$
$Express q as a ratio of factorials by observing that multiplying the integers from 200 through 299 is equivalent to dividing 299! by the product of integers from 1 through 199.$	$q = \frac{299 !}{199 !}$
$Form the quotient \frac{p}{q} using the expressions for p and q obtained in the previous steps.$	$\frac{p}{q} = \frac{\frac{299 !}{99 !}}{\frac{299 !}{199 !}}$
$Convert the complex fraction into a product by multiplying by the reciprocal of .$	$\frac{p}{q} = \frac{299 !}{99 !} \times \frac{199 !}{299 !}$
$Cancel the common 299! factors to arrive at the simplified expression.$	$\frac{p}{q} = \frac{199 !}{99 !}$

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The final answer is \frac{199 !}{99 !}, which corresponds to choice C.

The expression n! is defined as the product of the integers from 1 through n . If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to \frac{p}{q} ?

Explanation	Calculations	Help
$Express p as a ratio of factorials by observing that multiplying the integers from 100 through 299 is equivalent to dividing 299! by the product of integers from 1 through 99.$	$p = \frac{299 !}{99 !}$
$Express q as a ratio of factorials by observing that multiplying the integers from 200 through 299 is equivalent to dividing 299! by the product of integers from 1 through 199.$	$q = \frac{299 !}{199 !}$
$Form the quotient \frac{p}{q} using the expressions for p and q obtained in the previous steps.$	$\frac{p}{q} = \frac{\frac{299 !}{99 !}}{\frac{299 !}{199 !}}$
$Convert the complex fraction into a product by multiplying by the reciprocal of .$	$\frac{p}{q} = \frac{299 !}{99 !} \times \frac{199 !}{299 !}$
$Cancel the common 299! factors to arrive at the simplified expression.$	$\frac{p}{q} = \frac{199 !}{99 !}$

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The final answer is \frac{199 !}{99 !}, which corresponds to choice C.