In Exercises 23–28, evaluate each factorial expression. 16!/2!14!

Question

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 21 factorial divided by two factorial times 19 factorial. So I'm gonna go ahead and rewrite this In the fraction form off to the side here where I have 21 factorial in my numerator and two factorial times 19 factorial in my denominator. So recall that a factorial is the product of an integer and all the integers below it. So that means that I can rewrite 21 factorial as 21 times 20 factorial because this still includes 21 and all the integers below it. Since I have 20 factorial here and I can even expand this To be 21 times 20 times 19 factorial. So I'm going to go ahead and expand this to make it easier to simplify. So I'm going to rewrite the numerator. 21 factorial as 21 times 20 times factorial and my denominator will stay two factorial Times 19 factorial and here you can see that I have 19 factorial in both my numerator and denominator. So those cancel each other out to become one. So I'm left with 21 times Divided by two factorial and in this case to only has one integer below it which is one. So I have two times one in my denominator and I can cancel that out with this 20 it becomes a 10. So now I have 21 times 10. So that gives me 210. So and I can't when I simplify and evaluate the factorial expression I'm left with 2 10. So that becomes my final answer for this problem. And you can see that that aligns with answer choice. A So flee. This video helped and see you next time.

In Exercises 23–28, evaluate each factorial expression. 16!/2!14!

Watch next