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Flag Stripe Coloring Combinations

CAT 2004 Slot 1 · Quantitative Ability · Easy · Permutations and Combinations

This is an easy Quantitative Ability question from the CAT 2004 Slot 1 paper. It tests Permutations and Combinations. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done so that no two adjacent stripes have the same colour is:

  1. A.

    12×8112 \times 81

  2. B.

    16×19216 \times 192

  3. C.

    20×12520 \times 125

  4. D.

    24×21624 \times 216

Answer

A

Explanation

There are 44 available colors.

  • The 1st stripe can be colored in 44 ways.
  • The 2nd stripe can be colored in 33 ways (any color except the 1st).
  • The 3rd stripe can be colored in 33 ways (any color except the 2nd).
  • Each subsequent stripe up to the 6th can be colored in 33 ways. Total number of ways =4×35=4×243=12×81= 4 \times 3^5 = 4 \times 243 = 12 \times 81.

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