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Class 11MathematicsPermutations and CombinationsFundamental principle of countingHard
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A mobile unlock pattern uses (4) distinct points. The first point cannot be one of the (4) corner points. How many patterns are possible if there are (9) total points?

Answer and explanation

Correct answer: 1680

Of the 9 points, the 4 corner points are not allowed in the first position, so there are only 5 choices for the first point. The next three distinct points can then be chosen in 8, 7, and 6 ways respectively. Hence, the total number of patterns is \(5\times8\times7\times6=1680\). The value 1920 would result from incorrectly taking 8 choices instead of 5 for the first point. Exam tip: In pattern questions, order matters, so multiply the successive choices.

Related tags

Fundamental Counting PrinciplePermutationsMobile Unlock PatternDistinct ArrangementsClass 11 MathematicsFundamental Principle Of CountingPermutations And CombinationsMathematics
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