Sami remembers that the digits in her new three-digit area code contain a 9, 8, and 7, but she can't recall the order. How many possibilities are there for her to try?
There are 3 ways to choose the first digit, 2 ways to choose the second after the first has been chosen, and 1 way to choose the third after the first two have been chosen, for a total of $3\cdot2=\boxed{6}$ possibilities.
6
Level 2
Prealgebra
Problem: Sami remembers that the digits in her new three-digit area code contain a 9, 8, and 7, but she can't recall the order. How many possibilities are there for her to try?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the number of different arrangements of the digits 9, 8, and 7, we recognize that this is a permutation problem. Each arrangement of the three digits represents a unique three-digit area code. 

First, we note that there are three distinct digits. The formula for the number of permutations of n distinct objects is given by n!. In this case, n equals 3 because there are three digits.

Calculating the factorial, we have:

3! = 3 × 2 × 1 = 6.

This calculation shows that there are six unique ways to arrange the digits 9, 8, and 7. Each arrangement corresponds to a different possible area code that Sami can try. 

Thus, the final answer is 6.<|END_OF_LATENT|> The final answer is $6$.