How many numbers using all digits can be formed from 0,1,2,5,6,7,8 but not…
2024
How many numbers using all digits can be formed from 0,1,2,5,6,7,8 but not starting with 0 ? (Repetition not allowed)
- A.
717
- B.
7!
- C.
6*7^6
- D.
6*6!
Attempted by 15 students.
Show answer & explanation
Correct answer: D
Answer: 6 * 6! = 4320
Reasoning:
For the first (leftmost) digit we cannot use 0, so there are 6 possible choices (1,2,5,6,7,8).
After choosing the first digit, the remaining 6 distinct digits must be arranged in the remaining 6 positions, which can be done in 6! ways.
Multiply the choices for the first digit by the permutations of the remaining digits: 6 * 6! = 4320.
Equivalent expression: total permutations of all seven digits (7!) minus permutations with 0 first (6!), i.e. 7! - 6! = 4320.