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

Explanatory Answer

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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.

Correct Answer : 978

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