Question
Quantitative Aptitude Question on Permutations and Combinations
How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
A
50
B
45
C
60
D
65
Answer
50
Explanation
Solution
The sum of the digits must be a multiple of 3. We can use (A) 2,4,0,3 or (B) 2,4,0,6 or (C) 2,4,3,6
(A) _ _ _ 0 (6 numbers)
_ _ _ 2 (4 numbers)
_ _ _ 4 (4 numbers)
(B) _ _ _ 0 (6 numbers)
_ _ _ 2 (4 numbers)
_ _ _ 4 (4 numbers)
_ _ _ 6 (4 numbers)
(C) 2, 4, 3, 6 (18 numbers, with even digit in the units place)
There are a total of 50 numbers.