The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is __________ . [2023]

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Solution

Q.
The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is __________ . [2023]

Ans.
(60)

Even numbers are 2, 4, 2, 4

Odd numbers are 1, 3, 1, 3, 1

$\bar{O} \bar{E} \bar{O} \bar{E} \bar{O} \bar{E} \bar{O} \bar{E} \bar{O}$

$Even places can be filled with even numbers in \frac{4!}{2! 2!} ways.$

$Similarly, odd places can be filled in \frac{5!}{2! 3!} ways.$

$Required number of ways = \frac{4!}{2! 2!} \times \frac{5!}{2! 3!} = 60$

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