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
$$\therefore$$ 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
$$ = {{4!} \over {2!2!}} \times {{5!} \over {3!2!}} = 60$$
Comments (0)
