Question

How many four-digit different numbers, greater than $5000$ can be formed with the digits $1,2,5,9,0$ when repetition of digits is not allowed?

Answer 1

Given:

Available digits for filling any place ={$1,2,5,9,0$}

As the number has to be greater than $5000$,

The first digit can either be $5$ or $9$.

So, number of ways of filling the thousand’s

place $=2$

Number of ways of filling the hundred’s place $=4$

Number of ways of filling the ten’s place $=3$

[Since, repetition is not allowed]

Number of ways of filling the one’s place $=2$

By using the fundamental principle of Multiplication

$\therefore$ Total numbers
$=2\times 4\times 3\times 2$
$=48$

Hence,

Required number of four-digit numbers greater

than $5000$ are $48$.