- #1
archaic
- 688
- 214
- Homework Statement
- Let ##x## be the numbers of ways that a woman can wear ##5## distinct rings on ##5## fingers of her right hand, given that she can stack maximum of ##3## rings on any finger.
- Relevant Equations
- N/A
When she is stacking ##4## rings, then we have two objects; a configuration of ##4## rings, and a ring outside. The number of configurations is also given by ##5P5##. For the fingers, however, we now choose two fingers out of five to put the objects on, or, ##5P2##.
The same reasoning goes for the last case, so$$x=5P5(5P3+5P2+5P1)$$
EDIT: I understood the problem statement in a peculiar way. I don't know how that happened. However, the logic is kind of still the same, and I think$$x=5P5(5P5+5P4+5P3)$$
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