Question

Find the number of different 4 digit number can be formed using the digits 4, 9, 8, 6 and 7 such that the number is divisible by 3. (Repetition is not allowed)

• A. 24
• B. 48
• C. 72
• D. 96

Answer 1

The correct option is B 48

Number of ways selecting 4 digits from given five digits ${=}^5{C}_4=5$
i) 4, 9, 8, 6
ii) 4, 9, 8, 7
iii) 4, 8, 6, 7
iv) 9, 8, 6, 7
v) 9, 6, 7, 4

Divisibility rule for 3: The sum of the digits of the number should be divisible by 3.

i) 4, 9, 8, 6 = 27
ii) 4, 9, 8, 7 = 28
iii) 4, 8, 6, 7 = 25
iv) 9, 8, 6, 7 = 30
v) 9, 6, 7, 4 = 26

Only case 1 and case 4 satisfying the given condition.

4, 9, 8, 6 can be arranged in 4! Ways.
9, 8, 6, 7 can be arranged in 4! ways.

Total number of ways possible = 4! + 4! = 48