# Questionbank: Permutation and Probability

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Remember, we are looking for numbers that have a zero in them, not numbers that end in a zero.

## Non-Zero Numbers

Q.10: All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?
1. 25
2. 20
3. 35
4. 45

Choice D. 45

## Detailed Solution

Any multiple of 6 will end in a zero. There are 25 such numbers. Beyond this, we can have zero as the middle digit of a 3-digit number.

This will be the case for numbers from 37 - 41, 73 - 77, 109 - 113 and 145 - 149. There are 20 such numbers.

Overall, there are 45 numbers that have a zero in them.

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