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Subjects
Class 11MathematicsPermutations and CombinationsFundamental principle of countingMedium
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A school card is specified by a card type, a color, and a validity period. There are 4 card types, 5 colors, and 3 validity periods. For one particular card type, 2 of the colors are not allowed. How many valid cards are possible?

Answer and explanation

Correct answer: 54 cards

Without the restriction, there are 4 × 5 × 3 = 60 combinations. The restriction rules out 1 card type paired with 2 colors and any of the 3 validity periods, or 1 × 2 × 3 = 6 combinations. Thus, 60 − 6 = 54 valid cards are possible.

Related tags

Fundamental Counting PrincipleRestricted CountingFundamental Principle Of CountingPermutations And CombinationsMathematicsClass 11 Mcq
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