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Permutations with grouped items

CMAT 2018 · Quantitative Techniques & Data Interpretation · Medium · Permutations and Combinations

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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)

  1. A.

    1742

  2. B.

    1732

  3. C.

    1728

  4. D.

    1750

Answer

C

Explanation

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!=63! = 6. Internal arrangements within each group: Red balls: 3!=63! = 6 Blue balls: 2!=22! = 2 Yellow balls: 4!=244! = 24 Total ways = 3!×3!×2!×4!=6×6×2×24=17283! \times 3! \times 2! \times 4! = 6 \times 6 \times 2 \times 24 = 1728.

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