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Question
How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
Solution
The given digits are 0, 1, 2, 3, 4, 5
To find the possible 3-digit odd numbers.
Repetition of digits is not allowed:
| Hundred's | Ten's | Unit |
Since we need 3-digit odd numbers the unit place can be filled in 3 ways using the digits 1, 3 or 5.
Hundred’s place can be filled in 4 ways using the digits 0, 1, 2, 3, 4, 5 excluding 0 and the number placed in unit place.
Ten’s place can be filled in 4 ways using the digits 0, 1, 2, 3, 4, 5 excluding the digit placed in the hundred’s place.
Therefore, by the fundamental principle of multiplication
The number of 3 – digit odd numbers formed without repetition of digits using the digits 0, 1, 2, 3, 4, 5 is
= 4 × 4 × 3
= 48
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