There are $\binom{5}{4}$ different ways to choose 4 from 5 upper class soldiers. For each of these, there are $\binom{10}{8}$ ways to choose 8 lower class soldiers. The number of different battalions, then, is $\binom{5}{4}\cdot \binom{10}{8} = \boxed{225}$.
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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?
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225
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?
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