Question

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 7 flags that can be made using 3 white flags, 2 red flags, and 2 blue flags.

Answer 1

To find the number of different signals, we need to count the number of distinct arrangements of the 7 flags.

There are ${7 \choose 3} = 35$ ways to choose the positions of the white flags. Once the positions of the white flags are chosen, the positions of the red flags are uniquely determined, so we don't need to consider them. Once the positions of the white and red flags are chosen, the positions of the blue flags are also uniquely determined.

Therefore, the number of different signals is $\boxed{35}$.