How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9,…
2023
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
- A.
5
- B.
10
- C.
15
- D.
20
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Step-by-Step Solution
To form a 3-digit number from the set {2, 3, 5, 6, 7, 9} that is divisible by 5 without repeating digits, we follow these steps:
Divisibility Rule: A number is divisible by 5 if its units digit is either 0 or 5. Since 0 is not in our set, the units place must be filled by 5.
Number of choices for the units place: 1 (only '5').
Tens Place: After placing '5' in the units place, we have 5 remaining digits to choose from {2, 3, 6, 7, 9}.
Number of choices for the tens place: 5.
Hundreds Place: After filling the units and tens places, we have 4 remaining digits to choose from.
Number of choices for the hundreds place: 4.
Total Combinations: Using the fundamental counting principle, multiply the choices:
Total numbers = 1 (units) * 5 (tens) * 4 (hundreds) = 20.