\begin{tabular}{l} Perform the indicated calculation. \ $$ { }_{10} \mathrm{P}_{2} $$ \ \hline\end{tabular}

Question

UpStudy AI · Accepted Answer

To calculate $$ { }_{10} \mathrm{P}_{2} $$, we use the formula for permutations, which is given by:

$$
_{n}P_{r} = \frac{n!}{(n-r)!}
$$

In this case, $$ n = 10 $$ and $$ r = 2 $$.

Now, we can substitute these values into the formula:

$$
_{10}P_{2} = \frac{10!}{(10-2)!} = \frac{10!}{8!}
$$

Next, we can simplify $$ \frac{10!}{8!} $$:

$$
\frac{10!}{8!} = \frac{10 \times 9 \times 8!}{8!} = 10 \times 9
$$

Now, we can calculate $$ 10 \times 9 $$:

$$
10 \times 9 = 90
$$

Thus, the value of $$ { }_{10} \mathrm{P}_{2} $$ is $$ 90 $$.
The value of $$ { }_{10} \mathrm{P}_{2} $$ is 90.

\begin{tabular}{l} Perform the indicated calculation. \\ \( { }_{10} \mathrm{P}_{2} \) \\ \hline\end{tabular}