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Chapter 11: Problem 23

Evaluate each expression. \(1-\frac{{ }_{3} P_{2}}{{ }_{4} P_{3}}\)

Short Answer

Expert verified
The value of the expression \(1-\frac{{ }_{3} P_{2}}{{ }_{4} P_{3}}\) is 0.75

Step by step solution

01

Calculate the Permutations

First, calculate the permutation values for both \({ }_{3} P_{2}\) and \({ }_{4} P_{3}\). Using the formula given above, \({ }_{3} P_{2} = 3!/(3-2)! = 6/1 = 6\) and \({ }_{4} P_{3} = 4!/(4-3)! = 24/1 = 24\)
02

Substitute and Simplify

Next, substitute these values back into the original expression. So the expression becomes \(1 - \frac{6}{24}\) . Simplify that resulting expression by performing the division first (since in order of operations division comes before subtraction), obtaining \(1 - 0.25\)
03

Final Calculation

Finally, perform the subtraction and the result is \(0.75\)

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