Question

The number of numbers, greater than $400000$ that can be formed by using the digits $0,2,2,4,4,5$ is

• A. $90$
• B. $32$
• C. $20$
• D. None of these

Answer 1

The correct option is A $90$

There are $6$ digits and the numbers greater than $400000$ will have $6$ digits.

We have to use all $6$ digits at a time, the numbers greater than $400000$ will have either $4$ or $5$ at the extreme left position.

1. When $5$ is at the extreme left position, the remaining $5$ places can be filled with the digits $0,2,2,4,4.$

This can be done in $\frac{5!}{2!2!}=30$ ways

2. When $4$ occupies the extreme left position, then the remaining $5$ places can be filled by $0,2,2,4,5$ digits.

this can be done in $\frac{5!}{2!}=60$

So total numbers greater than $400000$ are $30+60=90$