Use the formula for ${}_n{P}_r$ to evaluate the following expression.
$${}_6{\mathrm{P}}_3$$
$${}_6{\mathrm{P}}_3=$$

Step 1 ：We are given the expression ${}_6{P}_3$ and we are asked to evaluate it.

Step 2 ：The formula for permutation is given by ${}_n{P}_r=\frac{n!}{(n-r)!}$ where 'n' is the total number of items, 'r' is the number of items to choose, 'n!' is the factorial of 'n', and '(n-r)!' is the factorial of the difference between 'n' and 'r'.

Step 3 ：In this case, 'n' is 6 and 'r' is 3. So, we need to calculate the factorial of 6, the factorial of (6-3), and then divide the two.

Step 4 ：First, calculate the factorial of 6, which is 720.

Step 5 ：Next, calculate the factorial of (6-3), which is 6.

Step 6 ：Finally, divide the factorial of 6 by the factorial of (6-3) to get the permutation. The result is 120.

Step 7 ：So, ${}_6{P}_3=\boxed{{\displaystyle 120}}$