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How many even three-digit numbers can be formed from the digits 1, 2, 5, 6 and 9 without repeating any of the digits ?
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- 120
- 48
- 40
- 24
- 120
Correct Option: D
The unit’s place will be occupied by 2 or 6 in three digit even numbers.
The remaining two places can be occupied by selecting from remaining four digits in 4P2 ways
4P2 = | = | = 12 | ||
(4 - 2)! | 2 |
∴ Total number of even three digit numbers = 2 × 12 = 24
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Total ways = 3 × 4 × 2 = 24 ways.
{∵ Total available digits are 1, 2, 5, 6, 9.
Even digits = 2 and 6.
⇒ A can either be filled by 2 or 6
i.e. 2 ways.
B can either be filled by 4 ways
[∵ Total – digit used at A i.e. 5 – 1]}
and C can either be filled by 3 ways
[Total – digit used at A – digit used at B i.e. 5 – 1 – 1]