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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
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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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