how many numbers each lying between 10 and1000 can be formed with digits 2 ,3,4,0,8,9 using only once????
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