# Questionbank: Permutation and Probability

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A combination of Probability and Number Theory gives a perfect question.

## Probability and Number Theory

Q.19: N is a 3-digit number that is a multiple of 7; what is the probability that it will be a multiple of 5?
1. 1/5
2. 11/54
3. 13/64
4. 13/66

Choice C. 13/64

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## Detailed Solution

N is a three digit multiple of 7.

N could be 105, 112, 119, 126…..994.

Or, 15 × 7, 16 × 7…..142 × 7.

Or there are 142–14 = 128 numbers.

Within these we need to locate the multiples of 5.

Or, we need to isolate multiples of 35.

Or, we need to see how many numbers there are in the list 105, 140, 175…..980.

35 × 3, 35 × 4…35 × 28…

Or, there are 26 such numbers.

Probability 26/128 = 13/64

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