Question 859719
how many numbers each lying between 10 and1000 can be formed with digits 2 ,3,4,0,8,9 using only once????
<pre>
Case 1:  two digit numbers:

We can choose the tens digit any of 5 ways (0 cannot be chosen)
We can then choose the units digit any of 5 ways, because
0 can be chosen.

That's 5×5 or 25 two digit numbers

Case 2:  three digit numbers:

We can choose the hundreds digit any of 5 ways (0 cannot be chosen)
We can then choose the tens digit any of 5 ways, because
0 can be chosen.
We can then choose the units digit any of the 4 remaining ways.

That's 5×5×4 = 100 three-digit numbers

Grand total: 25+100 = 125 

Edwin</pre>