What is the number of 6-digit numbers that can be formed from 0,1,5,6,7 and 8…
2024
What is the number of 6-digit numbers that can be formed from 0,1,5,6,7 and 8 in which the first digit is not 0 (No repetition allowed) ?
- A.
120
- B.
600
- C.
720
- D.
800
Attempted by 44 students.
Show answer & explanation
Correct answer: B
We must form 6-digit numbers using the digits 0, 1, 5, 6, 7, 8 with no repetition and the first digit not 0.
Choose the first digit (cannot be 0): any of 1, 5, 6, 7, 8 → 5 choices.
Arrange the remaining five digits in the other positions: 5! = 120 ways.
Total number = 5 × 5! = 5 × 120 = 600.
Alternate method: 6! − 5! = 720 − 120 = 600
Answer: 600