How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7, 9 that are divisible by 5 with no repeated digits?

Problem restatementForm 3-digit numbers from {2, 3, 5, 6, 7, 9} that are divisible by 5 and have no repeated digits.

Given data

• Available digits: 2, 3, 5, 6, 7, 9.
• Divisibility by 5 ⇒ last digit must be 5 (0 is not available).
• No repetition allowed.

Concept/ApproachFix the units digit as 5, then choose hundreds and tens from remaining distinct digits.

Step-by-step calculation Units digit = 5 (1 way) Hundreds digit = choose from {2, 3, 6, 7, 9} ⇒ 5 ways Tens digit = choose from remaining 4 digits ⇒ 4 ways Total numbers = 1 × 5 × 4 = 20

Verification/AlternativeListing logic shows structure H–T–5; choices reduce sequentially without repetition.

Final Answer20