Question

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?

Answer 1

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

${\Rightarrow }^{\prime }{0}^{\prime }$ 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 $\{0,1,2,3,4,5\}=5\times 5\times 4=100$.