A signal can be formed by running different colored flags up a pole, one above the other. Find the number of different signals consisting of 8 flags that can be made using 3 white flags, 3 red flags, and 2 blue flags. signals (Type a whole number.)

Step 1 ：This problem is a permutation problem with repetition. We have 8 flags in total, with 3 white flags, 3 red flags, and 2 blue flags. The total number of permutations of these 8 flags is \(8!\), but we have to divide by the number of ways we can arrange the white flags among themselves (\(3!\)), the red flags among themselves (\(3!\)), and the blue flags among themselves (\(2!\)) because they are indistinguishable.

Step 2 ：Calculate the total number of permutations of 8 flags, which is \(8! = 40320\).

Step 3 ：Calculate the number of ways we can arrange the white flags among themselves, which is \(3! = 6\).

Step 4 ：Calculate the number of ways we can arrange the red flags among themselves, which is \(3! = 6\).

Step 5 ：Calculate the number of ways we can arrange the blue flags among themselves, which is \(2! = 2\).

Step 6 ：Divide the total number of permutations by the number of ways we can arrange the white, red, and blue flags among themselves to get the number of different signals. This is \(\frac{40320}{6 \times 6 \times 2} = 560\).

Step 7 ：Final Answer: The number of different signals that can be formed is \(\boxed{560}\).