jmc

Question

The Greek army contained two types of soldiers: the upper class and the lower class soldiers. If there were a total of 5 upper class soldiers, and 10 lower class soldiers in a certain part of Athens, and the battle of Thermopylae demands a force of 4 upper class soldiers and 8 lower class soldiers, how many different battalions can be sent?

Accepted Answer

There are 54 different ways to choose 4 from 5 upper class soldiers. For each of these, there are 108 ways to choose 8 lower class soldiers. The number of different battalions, then, is 54 108 = 225.