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)

Question

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) (A) 7! 4! 5! 3! (B) 7! 4! (C) 7! 4! 5! 2! (D) 7! 4! 2!

Tardigrade Admin · Accepted Answer

Make 3 bundle each of same colour. Number of ways to arrange them =2 ! Total ways =(2 ! × 7 ! × 4 ! × 1/2)=7 ! 4 ! (as clockwise and anticlockwise are same)

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)

7! 4! 5! 3!

7! 4!

7! 4! 5! 2!

7! 4! 2!

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)

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)

7! 4! 5! 3!

7! 4!

7! 4! 5! 2!

7! 4! 2!

Make 3 bundle each of same colour. Number of ways to arrange them =2! Total ways =22!×7!×4!×1​=7!4! (as clockwise and anticlockwise are same)

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)