Determine the number of permutations (arrangements) possible of 10 things taken 2 at a time. The answer is

Step 1 ：The problem is asking to find the number of permutations possible of 10 things taken 2 at a time.

Step 2 ：The formula for permutations of n things taken r at a time is given by: \(P(n, r) = \frac{n!}{(n-r)!}\), where n! denotes the factorial of n.

Step 3 ：Substitute n = 10 and r = 2 into the formula: \(P(10, 2) = \frac{10!}{(10-2)!}\).

Step 4 ：Calculate the factorial of 10 and 8: \(10! = 3628800\) and \(8! = 40320\).

Step 5 ：Substitute these values into the formula: \(P(10, 2) = \frac{3628800}{40320} = 90\).

Step 6 ：Final Answer: The number of permutations possible of 10 things taken 2 at a time is \(\boxed{90}\).