Question

The number of ways of wearing 6 different rings on 5 fingers is:
 $
  (a)\,\,{5^6} \\
  (b)\,\,{6^5} \\
  (c)\,\,{5^5} \\
  (d)\,\,{6^6} \\
  $

Answer 1

Hint: To find the solution of this problem we use the concept of permutations. As it's given that any ring can be worn on any finger, so using this concept we first find a number of ways for one ring to be worn and then using it we can find the total number of ways.

Complete step-by-step answer:
Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.
Number of different rings = $ 6 $
Numbers of fingers = $ 5 $
As, there are $ 6 $ different rings that are to be worn in $ 5 $ fingers and there is no condition given in the question.
Therefore, for every ring there are $ 5 $ different ways available to put a ring in any finger.
So, for $ 6 $ different rings total number of available will be given as: $ {6^5} $
So, the correct answer is “Option B”.

Note: As, there is no condition given in the problem that how many rings can be worn in any finger, so one can put all rings in one finger or two, three or so. Hence, for each ring there are total five ways available as there are total five fingers given and hence for all six rings we can say total ways are equal to $ {6^5} $