Question

How many numbers greater than $10$lac be formed from $2,3,0,3,4,2,3$?

• A. $420$
• B. $360$
• C. $400$
• D. $300$

Answer 1

The correct option is B

$360$

The explanation for the correct option:

The total numbers can be formed.

For numbers greater than $10$ lacs there should be $7$ digits

We have $2,3,0,3,4,2,3$digits. and should begin with either$2$ or $3$or $4$.

The number of numbers if it starts with $2$ i.e. beginning with $2$ remaining $6$(Three $3\text{'}s$ are alike)

$\Rightarrow \frac{6!}{3!}=120$

Numbers starting with $3$i.e, beginning with $3$ remaining $6$ (Two $2\text{'}s$and two $3\text{'}s$are alike)

$\Rightarrow \frac{6!}{2!\times 2!}=180$

Numbers starting with $4$ i.e. beginning with $4$remaining $6$(Two $2\text{'}s$ and three $3\text{'}s$are alike)

$\Rightarrow \frac{6!}{3!\times 2!}=60$

Therefore, the total number of numbers formed

$=120+180+60=360$

Hence the correct option is B.