Problem 23 - College Algebra

Question

Evaluate each factorial expression. $$\frac{17 !}{15 !}$$

Step-by-Step Solution

Answer

The value of \( \frac{17!}{15!} \) is 272.

Step 1: Understand Factorials

Factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 17! = 17 × 16 × 15 × 14 × ... × 2 × 1.

Step 2: Break Down Terms

We break down the factorial terms one by one without actually calculating the values. So, \( \frac{17!}{15!} \) becomes \( \frac{17 × 16 × 15 × 14 × ... × 2 × 1 }{15 × 14 × ... × 2 × 1} \).

Step 3: Simplify Expression

As seen above, both numerator and denominator have common factors. They cancel each other. What's left in the expression after cancelling out the common terms would be \( \frac{17 × 16}{1} \).

Step 4: Calculate Result

After simplification we multiply the remaining non-cancelled terms in the numerator to get our result. That would be 17 * 16 = 272.