How many vehicle registration plate numbers can be formed with digits…
2026
How many vehicle registration plate numbers can be formed with digits 2,3,4,5,6 ( no digits being repeated ) if it is given that the registration number can have 1 to 5 digits ?
- A.
325
- B.
367
- C.
333
- D.
321
Attempted by 936 students.
Show answer & explanation
Correct answer: A
Answer: 325
Key idea: Count ordered arrangements (permutations) without repetition for each possible length from 1 to 5, then add the counts.
1-digit numbers: 5 ways (choose any of the 5 digits).
2-digit numbers: 5 × 4 = 20 ways (first digit any of 5, second any of remaining 4).
3-digit numbers: 5 × 4 × 3 = 60 ways.
4-digit numbers: 5 × 4 × 3 × 2 = 120 ways.
5-digit numbers: 5 × 4 × 3 × 2 × 1 = 120 ways.
Total possible registration numbers = 5 + 20 + 60 + 120 + 120 = 325.