How many 5-digit numbers can be formed using digits 1 to

Solution

We are to find how many 5-digit numbers can be formed using digits 1 to 5 without repetition, such that the number is divisible by 5. Digits available: 1, 2, 3, 4, 5 Total digits = 5 We are to form 5-digit numbers without repetition, and the number must be divisible by 5. A number is divisible by 5 only if it ends in 0 or 5. But we do not have 0, only digits {1, 2, 3, 4, 5}. So the number must end in 5. Fix 5 in the unit's place. Remaining digits = {1, 2, 3, 4} → 4 digits left to fill first 4 places. These 4 digits can be arranged in 4! = 24 ways