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Chapter 11: Problem 29

Evaluate each factorial expression. \(\frac{7 !}{(7-2) !}\)

Short Answer

Expert verified
The result of evaluating the factorial expression \(\frac{7 !}{(7-2) !}\) is 42.

Step by step solution

01

Simplify the Denominator

First the expression in the denominator needs to be simplified. Given \(\frac{7 !}{(7-2) !}\), calculate \(7-2\), which equals 5. So the initial expression becomes \(\frac{7 !}{5!}\).
02

Calculate the Factorials

7! equals 7 x 6 x 5 x 4 x 3 x 2 x 1 and 5! equals 5 x 4 x 3 x 2 x 1. You'll notice from both factorials, they share a common factors of 5 x 4 x 3 x 2 x 1. These can be cancelled out.
03

Simplify the Expression

After cancelling out, you're left with \(\frac{7 x 6}{1}\) which simplifies to \(7x6\) = 42.

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