JEE MAIN - Mathematics (2023 - 24th January Morning Shift - No. 21)

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 ______________.
Answer
60

Explanation

Here, even digits are 2 and 4.

Number of digit "2" presents = 2

Number of digit "4" presents = 2

$$\therefore$$ Total even digits = 4

JEE Main 2023 (Online) 24th January Morning Shift Mathematics - Permutations and Combinations Question 57 English Explanation

$$\therefore$$ Total 4 even places presents.

Number of ways to put those 4 digits in those 4 places $$ = {{{}^4{C_4} \times 4!} \over {2!2!}} = {{4!} \over {2!2!}}$$

Now, remaining 5 digits (three 1 and two 3) can be put in those 5 places in $$ = {{{}^5{C_5} \times 5!} \over {3!2!}} = {{5!} \over {3!2!}}$$ ways.

$$\therefore$$ Total possible 9 digit numbers

$$ = {{4!} \over {2!2!}} \times {{5!} \over {3!2!}} = 60$$

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