Questions: Find the value of the permutation. 3 P2 3 P2 = (Type a whole number.)

Solution Steps

To find the value of the permutation \({ }_{3} P_{2}\), we use the formula for permutations, which is given by \({ }_{n} P_{r} = \frac{n!}{(n-r)!}\). Here, \(n = 3\) and \(r = 2\). We will calculate the factorial of 3 and the factorial of \(3-2\), and then divide the two results to find the permutation value.

To find the value of the permutation \({ }_{3} P_{2}\), we use the formula for permutations: \[ { }_{n} P_{r} = \frac{n!}{(n-r)!} \] where \(n = 3\) and \(r = 2\).

We need to calculate \(3!\) and \((3-2)!\): \[ 3! = 3 \times 2 \times 1 = 6 \] \[ (3-2)! = 1! = 1 \]

Now, substituting the factorial values into the permutation formula: \[ { }_{3} P_{2} = \frac{3!}{(3-2)!} = \frac{6}{1} = 6 \]

Final Answer