Question

How many 3-digit numbers are there, with no digits repeated?

• A. 648
• B. 548
• C. 848
• D. 748
• E. None of these

Answer 1

The correct option is A 648

The required number of 3-digit numbers = The permutations of the 10 objects 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, taken 3 at a time, with the condition that 0 is not in the hundred's place.
$P=(10,3)-P(9,2)=\frac{10!}{7!}-\frac{9!}{7!}=\frac{10\times 9\times 8\times 7!}{7!}-\frac{9\times 8\times 7!}{7!}=10\times 9\times 8\times -9\times 8=720-72=648.$