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. Functions4h 53m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation2h 18m
4. Derivatives of Exponential & Logarithmic Functions1h 16m
- Derivatives of Exponential & Logarithmic Functions
  1h 16m
5. Applications of Derivatives2h 19m
6. Graphical Applications of Derivatives6h 0m
7. Antiderivatives & Indefinite Integrals48m
- Antiderivatives
  17m
- Indefinite Integrals
  31m
8. Definite Integrals4h 36m
9. Graphical Applications of Integrals1h 43m
- Area Between Curves
  1h 19m
- Introduction to Volume & Disk Method
  23m
10. Integrals of Inverse, Exponential, & Logarithmic Functions21m
- Integrals of Exponential Functions
  14m
- Integrals Involving Logarithmic Functions
  7m
11. Techniques of Integration2h 7m
- Integration by Parts
  1h 37m
- Improper Integrals
  29m
12. Trigonometric Functions6h 54m
13: Intro to Differential Equations2h 23m
14. Sequences & Series2h 8m
15. Power Series2h 19m
- Power Series & Taylor Series
  2h 19m
16. Probability & Calculus45m
- Continuous Probability Models
  45m

14. Sequences & Series

Review of Factorials

Business 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: Understand the factorial notation. 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 numerator of the given expression, which is 9!. Since the denominator includes 7!, you can cancel out the common terms in the numerator and denominator. This simplifies 9! / 7! to (9 × 8).

Step 3: Multiply the simplified numerator (9 × 8) by 7!. This results in (9 × 8 × 7!).

Step 4: Divide the result from Step 3 by the denominator, which is 2!. Recall that 2! = 2 × 1 = 2. So, divide (9 × 8 × 7!) by 2.

Step 5: Simplify the final expression by performing the division and multiplication. This will yield the final result.