Perform the indicated calculation. \[ \frac{{ }_{5} P_{2}}{{ }_{11} P_{4}} \] \[ \frac{{ }_{5} \mathrm{P}_{2}}{{ }_{11} \mathrm{P}_{4}}=\square \text { (Round to four decimal places as needed) } \]

Step 1 ：The problem is asking to calculate the ratio of two permutations. The permutation formula 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, and \(n!\) is the factorial of \(n\).

Step 2 ：So, we need to calculate \(_{5}P_{2}\) and \(_{11}P_{4}\), and then divide the first by the second.

Step 3 ：Calculating \(_{5}P_{2}\), we get 20.0

Step 4 ：Calculating \(_{11}P_{4}\), we get 7920.0

Step 5 ：Dividing the two results, we get a ratio of approximately 0.0025252525252525255

Step 6 ：Final Answer: The ratio of the two permutations is approximately \(\boxed{0.0025}\)