In Exercises 23–28, evaluate each factorial expression. 17!/15!

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Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to evaluate the factorial expression 23 factorial divided by 21 factorial. So in this case I'm going to rewrite this off to the side and more of a fraction format with 23 factorial in the numerator and 21 factorial in my denominator. And when working with factorial recall that a factorial is the product of an integer and all the integers below it. So for example three factorial is equal to three Times two Times 1. But I can also represent this as three times two factorial because two factorial is equal to two times one. So I'm gonna use this sort of property of factorial is to help me simplify this factorial expression more easily. I'm gonna rewrite my numerator as 23 times 22 times factorial And I'll keep my denominator denominator the same as 21 factorial. And from here you can see that I have 21 factorial in both the numerator and denominator of this fraction. So they cancel each other out to be one And I'm left with 23 times 22. When I do this multiplication I'm left with 506. So that means that 23 factorial divided by 21 factorial Evaluates to 506. So this becomes my final answer for this problem and you can see that this aligns with answer choice D. So hopefully this video helped. And see you next time

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In Exercises 23–28, evaluate each factorial expression. 17!/15!

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