In how many ways can we arrange 9 rings on 4 fingers of the right hand (excluding the thumb), if: (a) the rings are indistinguishable from each other and the fingers can also be empty? (b) we do not distinguish between the rings, but there must be at least one ring on each finger? (c) the rings are different, the order of the rings on the finger is not important, the fingers can also be empty?
In how many ways can we arrange 9 rings on 4 fingers of the right hand (excluding the thumb), if:
(a) the rings are indistinguishable from each other and the fingers can also be empty?
(b) we do not distinguish between the rings, but there must be at least one ring on each finger?
(c) the rings are different, the order of the rings on the finger is not important, the fingers can also be empty?
(d) the rings are different, the order of the rings on the finger does not matter, but there must be at least one ring on each finger?
(e) are the rings different, the order of the rings on the finger is important, can the fingers be empty?
(f) the rings are different, the order of the rings on the finger is important and there must be at least one ring on each finger?
The result should be given as an exact numerical value. Before calculating numerical values, give at least three examples of choices we can make. It uses Stirling numbers of the second order.
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but where is solution for d.), e.) and f.)??
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