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Chapter 11: Problem 15

Evaluate each factorial expression. \(\frac{29 !}{25 !}\)

Short Answer

Expert verified
The simplified value of \(\frac{29 !}{25 !}\) is \(26\cdot27\cdot28\cdot29 = 614088960\).

Step by step solution

01

- Understand the Properties of Factorials

To solve this exercise understanding the definition of a factorial is crucial. By definition, factorial of any non-negative integer \(n\), denoted by \(n!\), is the product of all the numbers less than or equal to \(n\). The expression given is \(\frac{29 !}{25 !}\). Here, the denominator \(25 !\) is part of the expression of the numerator \(29 !\), since \(29 !\) is the product of all numbers from 1 to 29.
02

- Simplify the Expression

Since the numerator and denominator share the same numbers up to \(25 !\), these values cancel out. The remaining expression now becomes \(26\cdot27\cdot28\cdot29\)
03

- Compute Remaining Factorials

Use multiplication to compute the product of the remaining factors, i.e., calculate \(26\cdot27\cdot28\cdot29\)

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