Question

How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?

Answer 1

Step 1: Choose the hundreds digit (first digit)

• Cannot be 0.

• From {1, 3, 5, 6} → 4 options

Step 2: Choose the tens digit (second digit)

• One digit is already used in hundreds place.

• Remaining digits = 4

• But includes 0 (which is now allowed) → So 4 options

Step 3: Choose the units digit (third digit)

• Two digits already used.

• Remaining digits = 3 → So 3 options

Total numbers = 4 (choices for first) × 4 (second) × 3 (third)

= 48