Question

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

• A. 36
• B. 48
• C. 60
• D. 72

Answer 1

Answer: (D)

72

Answer 2

Number should be divisible by 6 and it should be even.
Total sum = 1 + 2 + 3 + 5 + 6 + 7 = 24
So number removed should be of type 3.
Case-1 : excluding 3 $\rightarrow$ 2 ways = 4! × 2 = 24 × 2 = 48
Case-2: excluding 6 $\rightarrow$ 1 way = 4! = 24
Total cases = 48 + 24 = 72

So, the correct option is (D): 72