The number of five-digit numbers formed with the digits 0 , 1 , 2 , 3 , 4 and 5 (without repetition) and divisible by 6 are

Step-by-step solution

Divisible by six means divisible by 2 as well as 3 . (i) Case-1: without 0 ⇒ _ _ _ _ 2 / 4 _ So, we have to put 2 or 4 in ones place. ⇒ Number of ways = 4 _ × 3 _ × 2 _ × 1 _ × 2 _ = 2 × 4 ! = 48 (ii) Case-2: without 3 and 0 at ones place _ _ _ _ 0 _ ⇒ 4 × 3 × 2 × 1 × 1 = 4 ! = 2 4 (ii) Case-2: without 3 and 2 or 4 at ones place _ _ _ _ 2 / 4 _ ⇒ 3 × 3 × 2 × 1 × 2 = 3 6 ⇒ Total number of ways = 48 + 24 + 36 = 108