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Chapter 11: Problem 37

Use the formula for \({ }_{n} P_{r}\) to evaluate each expression. \({ }_{6} P_{6}\)

Short Answer

Expert verified
The value of \({ }_{6}P_{6}\) is 720.

Step by step solution

01

Identify the values of n and r

In the expression \({ }_{6}P_{6}\), the first number (6) is \(n\), which is the total number of items, and the second number (6) is \(r\), which is the number of items to select.
02

Calculate the factorial of n

Calculate the factorial of \(n\), which is \(6!\). The factorial of a number is the product of all positive integers from 1 up to that number. So, \(6! = 6 脳 5 脳 4 脳 3 脳 2 脳 1 = 720\).
03

Calculate the factorial of (n-r)

Calculate the factorial of \((n-r)\). In our case, \(n = r = 6\), so the calculation becomes \(0!\). The factorial of 0, \(0!\), is defined to be 1.
04

Substitute the values into the formula

Substitute the values obtained in steps 2 and 3 into the permutation formula: \({ }_{n}P_{r} = \frac{n!}{(n-r)!}\) becomes \({ }_{6}P_{6} = \frac{720}{1} = 720\).

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