# Questionbank: Permutation and Probability

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Numbers that are multiples of 2 and 3 are multiples of 6. Can we say numbers that are multiples of 4 and 6 are multiples of 24?

## Numbers with Distinct Digits

Q.12: How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6?
1. 975
2. 960
3. 978
4. 986

Choice C. 978

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## Detailed Solution

=> Single digit numbers: 1, 3 or 5: Three numbers

=> Two–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. So, there will be 3 × 5 = 15 such numbers.

=> Three–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. For the 100s’ digit, there are 4 choices {anything apart from what went into the units digit or tens digit}. So, there will be 3 × 5 × 4 = 60 such numbers.

=> 4–digit numbers: There will be 3 × 5 × 4 × 3 = 180 numbers.

=> 5–digit numbers: There will be 3 × 5 × 4 × 3 × 2 = 360 numbers.

=> 6–digit numbers: There will be 3 × 5 × 4 × 3 × 2 × 1 = 360 numbers.

Total number of numbers = 360 +360 + 180 + 60 + 15 + 3 = 978.

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