How many positive integers less than 500 can be formed using the digits 1, 2,…
2024
How many positive integers less than 500 can be formed using the digits 1, 2, 3, and 5, if each digit is used at most once?
- A.
37
- B.
56
- C.
34
- D.
50
Attempted by 567 students.
Show answer & explanation
Correct answer: C
Count by number of digits:
One-digit numbers: 4 choices (1, 2, 3, 5).
Two-digit numbers: 4 × 3 = 12 choices, because repetition is not allowed.
Three-digit numbers less than 500: the hundreds digit can be 1, 2, or 3 only. Then the tens and units digits can be chosen from the remaining digits: 3 × 3 × 2 = 18.
Total: 4 + 12 + 18 = 34.
Correct answer: 34