Permutation-Combination
Aptitude

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Q.

In how many ways can six different rings be worn on four fingers of one hand?

 A.

10

 B.

12

 C.

15

 D.

16

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Solution:
Option(C) is correct

Required number of ways,

$= {^6C_4}$

$= \dfrac{6 ×5}{2}$

$= \textbf{15 ways.}$


(13) Comment(s)


Pawan Kumar
 ()

there is no constraint on how many rings can be worn in single finger.

so,

(X+Y+Z+W) = 6

so, its same as how many solutions are there to this equation.

which is \binom{6+4-1}{4-1}



ABHIJEET
 ()

when different people have different answers..either the question is made up or the author doesn't know how to interpret the question..


ABHIJEET
 ()

the question should say in 'how many ways can four rings be selected from 6 rings to be worn on 4 fingers'


Payal
 ()

can anyone please tell it

each of 4 rings be worn in the index,ring finger and middle finger if there is no restriction of the number of rings to be worn on any finger?



Fran
 ()

Six DIFFERENT rings... that sounds to me like order matters and thus it should be 6P4



Kim
 ()

6 rings have 4 options of finger each so it will be [6][4].i.e. 1296



Dev
 ()

I think the solution should be 6x5x4x3=360 since there are 4 fingers to be filled.

The no. of ways that the first finger to be filled is 6 then for the next finger there will only be 5 since the first finger is already been filled the so on....


Anonymous
 ()

We should also select which 4 fingers of hand will have rings


Sanchit
 ()

answer should be $4^6= 4096$ as each ring has 4 alternative fingers in which they have to be placed as there is no restriction of no. of rings to be worn.

question should be more specific abt choosing of hand whether first of all 1 hand is to be chosen from 2 (in this case ans $2*4096$) or whether it is already selected.



Chandrasekaran
 ()

The right answer is 360 ways..

There are 4 fingers..

first finger has 6 possible ways of ring..

second finger has 5 third finger has 4 fourth finger has 3..

So $6*5*4*3=360$

could be answer



Sanjay
 ()

first the four fingers should be choose from five fingers $^5C_4 =5$ ways

answer should be $5*15= 75$



Arora
 ()

shouldn't the answer be $(^2C_1)*(4^6)$



Deepak
 ()

if 4 rings are choosen from 6 rings then its ok that the answer is 15 but the choosen rings can be worn in different fingers.so 15 must be multiplied with 4!.isnt't it?

kindly correct me if i'm wrong.