Through a marksmanship contest, there are 4 strings of 4 glass balls hanging down from a horizontal post. Each bullet can only hit one glass ball at a time, so 16 shots need to be fired.

The only problem is if you shoot a glass ball that has a glass ball hanging below it (on the same string), it will fall off. So given the rule that you can't shoot a glass ball with a glass ball underneath it (and on the same string), how many ways can you shoot all the glass balls?

The solution I heard to this is a great one in my opinion.

The idea is to plot out the order of the 16 balls getting shot down by strings and not by balls.
The 4 balls on the first string may take any of the 16C4 places. Then the 4 balls on the next string may take any of the remaining 12C4 places. Then the 4 balls on the next string may take any of the remaining 8C4 places, and the final string must take the remaining 4 places. When 16C4, 12C4 and 8C4 are all multiplied (C meaning _ combinations taken _ at a time), it comes out to 63,063,000.
(from "The Glass Balls")

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