The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1 , 2 , 3 , 4 , 5 , if the repetition of digits is not allowed and numbers are divisible by either 3 or 5 , is

Step-by-step solution

We need three digits numbers. Since 1 + 2 + 3 + 4 + 5 = 15 So, number of possible triplets for multiple of 15 is 1 × 2 × 2 so = 4 × ⌊ 3 + 4 × 3 - 1 × 2 × ⌊ 2 = 32 Alternate: divisible by 5 = 4 × 3 = 12 Divisible by 3 12 → 3 ,   4 ,   5 → 3 ! = 6 15 → 2 ,   3 ,   4 → 3 ! = 6 24 → 1 ,   3 ,   5 → 3 ! = 6 42 → 1 ,   2 ,   3 → 3 ! = 6               &#1