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Question

A seven digit number is formed by using 0,1,2,3,4,8,9 without repetition. Then the probability that it is divisible by 4 is

A
53×4!5×6!
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B
53180
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C
536×6!
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D
None of these
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Solution

The correct option is B 53180
Two or more than two digit number will be divisible by 4 if its last two
digit are divisible by 4 so we need the number of the form 04, 08, 12,
24, 28, 32, 40, 48, 80, 84, 92. There are twelve cases out of which in 5
cases like 04, 08, 20, 40, 80, total numbers are =5×5! and numbers in other 7 cases are 4×4!×7
Number of favorable cases are =5×5!+4×7×4! =(25+28)4!=53×4!
Total number of 7 digit number =7!6!=6.6!
Required probability
=53×4!6×6×5×4!=53180

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