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  • Number of different types of garlands that can be formed using 6 different flowers, of which three are of same colour such that flowers of same colour are together is<st

Number of different types of garlands that can be formed using 6 different flowers, of which three are of same colour such that flowers of same colour are together is

Option: 1

6 


Option: 2

18 


Option: 3

36 


Option: 4

72 


Answers (1)

best_answer

As we have learned,

Rule for Circular Permutations

Arrangement of NECKLACE, GARLAND are non distinct in clockwise and anti-clockwise: So number of arrangement =\frac{(n-1)!}{2}     

 

Now,

Let us tie 3 flowers of same colour in one unit , so the number of units on garland will be 4 

No. of ways of arranging these units in a circle = (4-1) ! * 3 ! (flowers of same colour will also arrange mutually )

But , clockwise and anticlockwise are non - distinct here , 

Required number of ways  = \frac{3 ! \times 3 ! }{2} = 18

Posted by

avinash.dongre

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