permutations

Question

The number of ways in which 6 rings can be worn on the four fingers of one hand is:

a. 360

b. 4^6

c. 6C4

d. 6^4

Comments

Let x₁ be the no. of rings on first finger, x₂ on second,x₃ on third and x₄ on fourth, then

x₁ + x₂ + x₃ + x₄ = 6

using C(n+r-1,r) 

the solution is 9C₆ = 84

what is wrong in this approach?

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I think it is more accurate

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But the answer does not match to any of the options.. Moreover I could not find the difference between the two approches

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if you use this method , ring should be identical .. which is not mentioned

Answer 1

Ans B) option, you can put one ring in any of 4 fingers so it becomes 4*4*4*4*4*4.

Comments

Thanks. But my approach about this question is : we have to select 4 rings out of 6 rings. and then we have 4! arrangements. so the result is : 6C4  * 4!  = 360

Could you please tell me where i'm going wrong?

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What you are doing is permutation without repetition means only one ring on one finger, but there is no such constraint in the ques. So 4^6 is the ans which is permutation with repetition allowed.

Answer 2

Case(1) When all rings are same

x1+x2+x3+x4=6

C(n+r-1,r) =9C6 

              =84

Case(2) All are distinct n u require all rings to worn

then C(n+r-1,r)*n! =9C6*6!

                                                     =60480