How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?
The numbers lying between 100 & 1000 are 3 digit numbers .We are to form 3 digit numbers between 100 & 1000 such that there's no repitition.
We have six different digits 0,1,2,3,4,5 to be filled in three vacant places.
Since we have to form three digit number
⇒′0′ cannot be in the hunderdth place .
So the 100th place can be filled in 5 ways .
Now having filled the 100th place,we are left with 5 numbers for the 10th place i.e.,10th place 100 can be filled in 5 ways.
And the one's place can be filled with 4 different numbers .
By the fundamental principle of counting, the required number of numbers lying between 100 & 1000 formed out of {0,1,2,3,4,5}=5×5×4=100.