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Question
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
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Solution
The given numbers are 1, 1, 2, 3, 3, 4
| Unit |
In order to get even 6-digit numbers
The unit place must be filled by the digits 2 or 4.
Therefore, the unit place can be filled in 2 ways using the digits 2 or 4.
In the remaining 5 digits (excluding the digit placed in the unit place 2 or 4) 1 occurs 2 times, 3 occurs 2 times.
∴ The number of ways of filling other places using the remaining 5 digit is = `(5!)/(2! xx 2!)`
∴ Number of distinct 6-digit numbers = `(5!)/(2! xx 2!) xx 2`
`(5!)/(2! xx 2!)`
= 5 × 4 × 3
= 60
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