In Exercises 23–28, evaluate each factorial expression. 17!/15!
Verified step by step guidance
1
Understand that a factorial, denoted by an exclamation mark (!), is the product of all positive integers up to a given number. For example, \( n! = n \times (n-1) \times (n-2) \times \ldots \times 1 \).
Recognize that the expression \( \frac{17!}{15!} \) involves dividing two factorials.
Notice that \( 15! \) is a common factor in both the numerator and the denominator, so it can be canceled out.
After canceling \( 15! \), you are left with \( 17 \times 16 \). Multiply these two numbers to find the result.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factorial Definition
A factorial, denoted by n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in permutations, combinations, and various mathematical calculations, making them fundamental in algebra and higher mathematics.
When evaluating expressions involving factorials, simplification can be performed by canceling common terms. For instance, in the expression 17!/15!, we can express 17! as 17 × 16 × 15!, allowing us to cancel the 15! in the numerator and denominator, simplifying the calculation significantly.
Factorials have specific properties that can aid in calculations, such as n! = n × (n-1)! and 0! = 1. Understanding these properties allows for easier manipulation of factorial expressions, especially when dealing with larger numbers or complex expressions in algebra.