Questions: Evaluate the expression. 5 P4 1 15 120 0

Solution Steps

To evaluate the permutation \({ }_{5} \mathrm{P}_{4}\), we need to use the formula for permutations, which is given by: \[ { }_{n} \mathrm{P}_{r} = \frac{n!}{(n-r)!} \] Here, \(n = 5\) and \(r = 4\). We will calculate the factorial of 5 and the factorial of (5-4), then divide the two results.

To evaluate the permutation \({ }_{5} \mathrm{P}_{4}\), we use the formula: \[ { }_{n} \mathrm{P}_{r} = \frac{n!}{(n-r)!} \] where \(n = 5\) and \(r = 4\).

Calculate the factorial of \(n\) and \((n-r)\): \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \] \[ (5-4)! = 1! = 1 \]

Substitute the factorial values into the permutation formula: \[ { }_{5} \mathrm{P}_{4} = \frac{5!}{(5-4)!} = \frac{120}{1} = 120 \]

Final Answer