JEE Main 2014 (Online) 12th AprilQuestion 1
$8$-digit numbers are formed using the digits $1,1,2,2,2,3,4,4$. The number of such numbers in which the odd digits do not occupy odd places, is :
Permutation and Combination
Solution
Concept. The odd digits $1,1,3$ cannot use odd places, so they go into the $4$ even places. Formulas used. (1) ${}^4C_3=4$(2) Arrangements with repeats: $\frac{n!}{p!\,q!}$Step 1 - Even places. Places $2,4,6,8$: $4$. Step 2 - Odd digits. Choose $3$ of them: $4$; arrange $1,1,3$: $\frac{3!}{2!}=3$. Total $12$. Step 3 - Rest. $2,2,2,4,4$ in the remaining $5$ places: $\frac{5!}{3!\,2!}=10$. Step 4 - Multiply. $12\cdot10=120$. Answer: B