JEE Main 2023 (Online) 24th January Morning ShiftQuestion 1
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 ______
Permutation and Combination
Answer$60$
Solution
Concept. 123412341 has digits $1,1,1,2,2,3,3,4,4$. The 4 even digits $2,2,4,4$ must go into the 4 even places. Formulas used. (1) Arrangements with repeats: $\dfrac{n!}{p!\,q!}$Step 1 - Even places 2, 4, 6, 8. $2,2,4,4$: $\frac{4!}{2!\,2!}=6$. Step 2 - Odd places 1, 3, 5, 7, 9. $1,1,1,3,3$: $\frac{5!}{3!\,2!}=10$. Step 3 - Total. $6\cdot10=60$. Answer: 60