IIT JEE , AIEEE Forum - Mathematics , Algebra - The number of numbers are there between 100 and 1000 in which all the digits are distinct

vaibhavmadamshetty

The number of numbers are there between 100 and 1000 in which all the digits are distinct is

konichiwa2x

Let x y z be the number.
Any one of the nine digits from 1 to 9 can be the value of 'x' . But for 'y' , zero can also be a choice. Hence if there was no restriction on the number, 'y' could have assumed 10 different numbers. Now we know that, whatever value was chosen for 'x', the same value cannot be chosen for 'y'. hence only 9 possibilities remain for 'y'. Similarly, 8 different possibilities are there for 'z'.

Hence there 9 x 9 x 8 = 648 such numbers.

spideyunlimited

Let the number be _ _ _
First place can be filled in 9 ways : 1 to 9
2nd place again in 9 ways : omitting the digit used in irst place but now we can use 0 also.
3rd place: 8 ways as we now we have one digit lesser than earlier if we want to prevent repitition.
so answer is 9 x 9 x 8 = 648 such numbers. :)

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