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Find the value of the following. (6!10!)/(7!9!)

Question:

Find the value of the following.

{eq}\frac{6!10!}{7!9!} {/eq}

Dividing Factorials:

If we divide two factorials, the smaller factorial will get canceled out and the product of the numbers exceeding the smaller factorial will remain in the numerator or denominator, depending on where the larger factorial is located in. So, simplifying a rational expression having multiple factorials both in the numerator and denominator can simply be done by cancelling common factors.

Answer and Explanation: 1

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Cancelling out common factors of {eq}6! {/eq} and {eq}7! {/eq} will leave us with {eq}7 {/eq} in the denominator as only {eq}7 {/eq} exceeds...

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Division of Factorials: Definition & Concept

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Chapter 13 / Lesson 9
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Factorial functions are commonly used to calculate the possible ways objects can be arranged and grouped. Learn how to express factorial functions with factorial notations, divide with factorial functions in the numerator and/or denominator, and solve permutation and combination problems.


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