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Question
A five digit number is formed with the digits 0,1,2,3,4 without repetition. The probability that it is a number divisible by 4
A five digit number is formed with the digits 0,1,2,3,4 without repetition. The probability that it is a number divisible by 4
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Solution
The correct option is B 5/16
The number will be divisible by 4 when its last two digits are divisible by 4.
Now that means number has to be even.So last digits has to be 0 ,2,4
When the last digit is 0 , then the number at tens place can be 2,4 so that makes it 2∗3!
Now when the last digit is 2 the number at ens place can be 1,3 so the number of ways of getting 5 digit number whose last two digtis are 32 or 12 ="4*2"
Similarly when last digit is 4 ...number at tens can be 2,0 so number of ways when last two digits are 04=3!
For last two digits to be 24 we get number of ways as 2∗2∗1=4
Total number of desirable outcomes = 30
Total outcomes =4∗4!
probability=30/96=5/16
The number will be divisible by 4 when its last two digits are divisible by 4.
Now that means number has to be even.So last digits has to be 0 ,2,4
When the last digit is 0 , then the number at tens place can be 2,4 so that makes it 2∗3!
Now when the last digit is 2 the number at ens place can be 1,3 so the number of ways of getting 5 digit number whose last two digtis are 32 or 12 ="4*2"
Similarly when last digit is 4 ...number at tens can be 2,0 so number of ways when last two digits are 04=3!
For last two digits to be 24 we get number of ways as 2∗2∗1=4
Total number of desirable outcomes = 30
Total outcomes =4∗4!
probability=30/96=5/16
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