Questions: Evaluate the expression. If the answer is not an integer, round to four decimal places. 10 P2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value is not an integer, 10 P2= . (Round to four decimal places as needed.) B. The value is an integer, 10 P2= . (Type an integer.)

Evaluate the expression. If the answer is not an integer, round to four decimal places. 10 P2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value is not an integer, 10 P2= . (Round to four decimal places as needed.) B. The value is an integer, 10 P2= . (Type an integer.)
Transcript text: Evaluate the expression. If the answer is not an integer, round to four decimal places. \[ { }_{10} P_{2} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value is not an integer, ${ }_{10} \mathrm{P}_{2}=$ $\square$ . (Round to four decimal places as needed.) B. The value is an integer, ${ }_{10} \mathrm{P}_{2}=$ $\square$ . (Type an integer.)
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Solution

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Solution Steps

Step 1: Calculate the number of permutations

Using the formula for permutations, $nPr = \frac{n!}{(n-r)!}$, with $n=10$ and $r=2$, we get: $$nPr = \frac{10!}{(10-2)!} = 90$$

Final Answer:

The number of permutations of 10 items taken 2 at a time is 90.

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