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?

Label the strings A, B, C and D.

When a given string is shot at, there's no choice as to which ball on the string to hit, so the number of ways is just the ways of rearranging four A's, four B's, four C's and four D's, which is:

16!/(4!*4!*4!*4!) = 63,063,000

Posted by Charlie on 2004-01-30 14:37:03