Question

The number of six digited numbers between $1,00,000$ and $3,00,000$ which are divisible by 4 and formed by rearranging digits of $112233$ is:

• A. 12
• B. 15
• C. 18
• D. 19

Answer 1

The correct option is A 12

Six numbered digit by rearranging $112233$

But the number should be between $1,00,000$ and $3,00,000$

Hence we are arranging $33$ such that the number will not start from $3$

Hence now we have to arrange only four digits $1122$

But here we have another condition that the number should be divisible by $4$

Hence we are arranging last 2 digit such that the number formed will be divisible by 4

Hence

No of ways $={}^4{C}_2\times 2$

No of ways $=\frac{4!}{2!2!}\times 2$

No of ways $=\frac{4\times 3}{2}\times 2$

No of ways $=12$