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Question

Number of 4 digit numbers that can be formed using the digits 0,1,2,3,4,5 which are divisible by 6 when repetition of digits is not allowed are

A
24
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B
52
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C
72
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D
48
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Solution

The correct option is B 52
For any number to be divisible by 6 the number should be even and divisible by 3.
Now, for number to be even the last digit should be 0,2,4.

Now, if the last digit is 0 then first 3 digits can be (1,2,3) or (2,3,4) or (3,4,5) or (1,3,5).
So, possible numbers are =4×3!=24

Now, if the last digit is 2 then first 3 digits can be (0,1,3) or (0,3,4) or (1,4,5).
So, possible numbers are =4+4+3!=14

Now, if the last digit is 4 then first 3 digits can be (0,2,3) or (0,3,5) or (1,2,5).
So, possible numbers are =4+4+3!=14

Hence, total numbers are 14+14+24=52

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