Question

Find the number of numbers that are greater than 4000 which can be formed using the digits 2,3,4,5,6 without repetition.

Answer 1

We are having digits $2,3,4,5$ and $6$. Numbers greater than $4000$ are to be formed using these digits without repetition.

The number can have $4$ digits but greater than $4000$ or can have $5$ digits.

Total number of $4$ digits number greater than $4000$ are,

$\Rightarrow 3{\times }^4{P}_3=3\times 24=72$

Total number of $5$ digits numbers ${=}^5{P}_5=5!=120$

So,

Total number of required numbers $=120+72=192$

Hence, this is the required result.