### Home > A2C > Chapter 11 > Lesson 11.2.3 > Problem11-75

11-75.

Before radios and satellite communication systems, ships would communicate with each other by using a string of colored flags. With four blue flags and two red flags, how many six flag signals are possible?

There are multiple ways to solve this problem. One way is to think of it as choosing positions for each of the flags.

Imagine there are six positions that the flags can occupy, and you have chosen positions for the red flags. How many ways can you choose positions for the blue flags, given that order does not matter?

$\Large{_{6}C_{2} = 15}$