Question

How many numbers greater than $40000$ can be formed using the digits $1,2,3,4$ and $5$ if each is used only once in a number?

Answer 1

The given digits are $1,2,3,4$ and $5$ which are $5$ in number.

As the number $40000$ has five digits and the numbers greater than $40000$ are to be formed by using each of the given digit only once, the numbers of only five digits are to be formed.

Ten thousands place can be filled up by any of the digits $4$ or $5$ in $2$ different ways.

Remaining $4$ places can be filled up by the remaining $4$ digits in ${}^4{P}_4$ ways.

$\Rightarrow$ The required number of numbers$=2{\times }^4{P}_4=2\times 4!=2\times 4\times 3\times 2\times 1=48$