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  4. The number of ways in which 7 different red roses 4 different blue roses and 5 alike green roses can form a garland so that flowers of same colour should be together, is (Do not distinguish clockwise and anticlockwise circular permutation)

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Q. The number of ways in which 7 different red roses 4 different blue roses and 5 alike green roses can form a garland so that flowers of same colour should be together, is (Do not distinguish clockwise and anticlockwise circular permutation)

Permutations and Combinations

Solution:

Make 3 bundle each of same colour. Number of ways to arrange them $=2 ! $
Total ways $=\frac{2 ! \times 7 ! \times 4 ! \times 1}{2}=7 ! 4 !$ (as clockwise and anticlockwise are same)