How many three 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?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20
A number is divisible by 5 only if its last digit is 0 or 5. There is no 0 among the digits, so the units place must be 5; the other two places are then filled from the remaining digits without repeating.
Units place: only 5, so 1 way
Hundreds place: any of the other 5 digits (2, 3, 6, 7, 9), so 5 ways
Tens place: any of the 4 digits still left, so 4 ways
Number of such numbers \(=5\times4\times1=20\)