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Chapter 11: Problem 16

Evaluate each factorial expression. \(\frac{31 !}{28 !}\)

Short Answer

Expert verified
The value of the expression \(\frac{31 !}{28 !}\) is 26970.

Step by step solution

01

Understanding Factorials

Recall that factorial of a number is the product of all positive integers less than or equal to that number. For example, 5! = 5*4*3*2*1. So \(31 ! = 31*30*29*...*3*2*1\) and \(28 ! = 28*27*...*3*2*1\).
02

Break Down and Simplify

Given the number \(\frac{31 !}{28 !}\), we can simplify it by cancelling out the common terms. We rewrite it as \(31*30*29*28 *...*3*2*1 / 28*...*3*2*1\). You see that \(28!*...*3*2*1\) terms are common in both the numerator and the denominator and can thus be cancelled.
03

Computation

After cancelling out the common terms, we are left with \(31*30*29\) in the numerator. So our expression simplifies to \(31*30*29\) which comes out to be 26970.

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