Evaluate the expression. 9 ! 7 ! \frac{9!}{7!} 7 ! 9 !

Here we're asked to evaluate the expression and the expression we're given is nine factorial over seven factorial. Now your instinct might be to fully expand both the numerator and the denominator here, but remember that we can actually write this in a way that we're going to be able to cancel some stuff and make this easier for us. So let's go ahead and do that. Now remember that any factorial is just a new number multiplied by the previous factorial. So whenever I'm writing out and expanding my numerator here, I can actually write this as nine times eight times seven factorial because I see on the bottom that I have seven factorial so this will allow me to cancel that. So once I'm here, I can actually just fully get rid of the seven factorial on the top and the bottom. Those are going to cancel leaving me with just nine times eight. So nine times eight is equal to 72 which gives me my final answer that nine factorial over seven factorial is equal to 72. Thanks for watching and I'll see you in the next one.

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0. Functions7h 52m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation3h 18m
4. Applications of Derivatives2h 38m
5. Graphical Applications of Derivatives6h 2m
6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
7. Antiderivatives & Indefinite Integrals1h 26m
8. Definite Integrals4h 44m
9. Graphical Applications of Integrals2h 27m
- Area Between Curves
  1h 18m
- Introduction to Volume & Disk Method
  1h 8m
10. Physics Applications of Integrals 3h 16m
- Kinematics
  1h 13m
- Work
  2h 3m
11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
12. Techniques of Integration7h 39m
13. Intro to Differential Equations2h 55m
14. Sequences & Series5h 36m
15. Power Series2h 19m
- Introduction to Power Series
  1h 9m
- Taylor Series & Taylor Polynomials
  1h 10m
16. Parametric Equations & Polar Coordinates7h 58m

14. Sequences & Series

Review of Factorials

Calculus

14. Sequences & Series

Review of Factorials

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Multiple Choice

Evaluate the expression.
$\frac{9!}{7!}$

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Verified step by step guidance

Step 1: Recognize that the problem involves factorials. Recall that the factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n. For example, 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Step 2: Simplify the given expression $ \frac{9!}{7!} $. Notice that $ 9! = 9 \times 8 \times 7! $, so the $ 7! $ in the numerator and denominator cancel out, leaving $ 9 \times 8 $.

Step 3: Divide the result from Step 2 by $ 2! $. Recall that $ 2! = 2 \times 1 = 2 $. So, the expression becomes $ \frac{9 \times 8}{2} $.

Step 4: Simplify $ \frac{9 \times 8}{2} $ by performing the division. Divide $ 8 $ by $ 2 $, which simplifies the expression to $ 9 \times 4 $.

Step 5: Multiply $ 9 \times 4 $ to find the final result. This gives the value of the expression.