Evaluate the permutation.
\[
{ }_{13} \mathrm{P}_{10}
\]
Answer
Thus, the permutation of 13 items taken 10 at a time is \(\boxed{1037836800}\).
Step 1 ：We are given a permutation problem, where we need to find the number of ways to choose 10 items from a total of 13 items. The formula for permutation is given by \(nPr = \frac{n!}{(n-r)!}\), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 2 ：In this case, n = 13 and r = 10. So we need to calculate the factorial of 13 and 3 (since 13 - 10 = 3), and then divide the factorial of 13 by the factorial of 3.
Step 3 ：The factorial of 13 is 6227020800 and the factorial of 3 is 6.
Step 4 ：Substituting these values into the permutation formula, we get \(nPr = \frac{6227020800}{6} = 1037836800\).
Step 5 ：Thus, the permutation of 13 items taken 10 at a time is \(\boxed{1037836800}\).
