Question

How many five-digit numbers, which do not contain identical digits, can be written by means of the digits $1,2,3,4,5,6,7,8$ and $9$?

Answer 1

We have 9 digits and 5 slots to create a 5-digit number.

$-----\uparrow$

First slot has 9 possible choices out of $1,2,3,4,5,6,7,8$ and $9$.so it can be filled in 9 ways.

$-----\uparrow$

Second slot is now,left with 8 choices.so it can be filled in 8 ways.

Similarly,third,fourth and fifth can be filled in 7, 6 and 5 ways respectively.

To get all possible permutations,just multiply these numbers i.e, $9\times 8\times 7\times 6\times 5=15120$