Question

In how many different ways can 3 red balls, 2 blue balls and 4 yellow balls be arranged so that the balls of the same color come together? (Consider the balls are not identical except for the colour)

Accepted Answer

C. Group each color of balls as one single unit. There are 3 groups (Red, Blue, Yellow). Number of ways to arrange the 3 groups = $3! = 6$. Internal arrangements within each group: Red balls: $3! = 6$ Blue balls: $2! = 2$ Yellow balls: $4! = 24$ Total ways = $3! 	imes 3! 	imes 2! 	imes 4! = 6 	imes 6 	imes 2 	imes 24 = 1728$.

Permutations with grouped items

Explanation

Practise this under exam conditions