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Subjects
Class 11MathematicsPermutations and CombinationsFundamental principle of countingMedium
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A sequence has 6 positions, and 5 colors are available. No two consecutive positions may have the same color. How many sequences are possible?

Answer and explanation

Correct answer: 5120 sequences

The first position has 5 choices. Each of the remaining 5 positions has 4 choices, since it must differ from the color immediately before it. Therefore, the number of sequences is 5 × 4⁵ = 5120.

Related tags

Counting PrincipleRestrictionsFundamental Principle Of CountingPermutations And CombinationsMathematicsClass 11 Mcq
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