SOLUTION: One fateful evening, seven different fires erupt around town. The local fire station houses 21 distinct fire trucks. The fire chief is instructed to dispatch exactly three trucks t
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Question 1115780: One fateful evening, seven different fires erupt around town. The local fire station houses 21 distinct fire trucks. The fire chief is instructed to dispatch exactly three trucks to fight each of the blazes. In how many ways can the trucks be dispatched ?
In the above problem, suppose the fire chief is to dispatch all 21 trucks, but there are no requirements on how many trucks must visit any given fire. Now how many choices does the fire chief have ? Answer by ikleyn(52778) (Show Source):
Under the given condition, the chief can dispatch 1-st truck to any of 7 fires: 7 opportunities;
2-nd truck to any of 7 fires: 7 opportunities;
3-rd truck to any of 7 fires: 7 opportunities;
4-th truck to any of 7 fires: 7 opportunities;
. . . . . . . . . . . and so on . . . . . . . . . .
21-th truck to any of 7 fires: 7 opportunities.
In all, there are different ways.
