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Question

Two natural numbers are chosen at random from the first one hundred natural numbers. The probability that the product of the chosen numbers is a multiple of 7 is.

A

14C1×13C1100C2

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B

14C2100C2+14C1 13C1100C2

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C

14C1 86C1100C2+14C2100C2

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D

14C2100C2+7C1 14C1100C2

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Solution

The correct option is C 14C1 86C1100C2+14C2100C2 Out of the 100 natural numbers, 14 numbers are multiples of 7. These exists two cases. Case 1: The product is a multiple of 7 if one of the number is in the form of 7k. ⇒14C1×86C1100C2 Case 2: The product is a multiple of 7 if both the numbers are in the form of 7k. ⇒14C2100C2 ∴ Probability =14C1 86C1100C2+14C2100C2

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