Question

How many numbers are there between 100 and 1000 in which all thevdigits are distinct?

Answer 1

QUESTION


How many numbers are there between 100 and 1000 in which all thevdigits are distinct?


ANSWER

100,101,102,........


999,1000.




We know that numbers between 100 and 1000 will be 3 digit integers. 

so,

Let the arrangement be ABC where A,B,C represent distinct digits.


Now there are 10 number from which all digit form

0,1,2,3,4,5,6,78,9.

but a never can be started by 0

We have 9 options for A (as 0 can not start a 3 digit number)

for B we have 9 options( because number are distinct )

and 8 for C,. (because number are distinct)


SO,




Numbers are there between 100 and 1000

$= 9 \times 9 \times 8$



$= 648$