Questions: Use the formula for nPr to evaluate the following expression. 18P0 18P0 = □

Solution Steps

To solve the problem of evaluating the permutation expression \({ }_{18} \mathrm{P}_{0}\), we use the formula for permutations, which is given by:

\[ { }_{n} \mathrm{P}_{r} = \frac{n!}{(n-r)!} \]

In this case, \(n = 18\) and \(r = 0\). Substituting these values into the formula, we get:

\[ { }_{18} \mathrm{P}_{0} = \frac{18!}{(18-0)!} = \frac{18!}{18!} = 1 \]

The formula for permutations is given by:

\[ { }_{n} \mathrm{P}_{r} = \frac{n!}{(n-r)!} \]

In this problem, we have \(n = 18\) and \(r = 0\). Substituting these values into the permutation formula, we get:

\[ { }_{18} \mathrm{P}_{0} = \frac{18!}{(18-0)!} = \frac{18!}{18!} \]

Since \( \frac{18!}{18!} = 1\), we find that:

\[ { }_{18} \mathrm{P}_{0} = 1 \]

Final Answer