Question

# The number of odd numbers greater than 8000 that can be formed using the digits 2,3,4,5 and 8, if repetition is not allowed is

A
60
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B
65
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C
24
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D
12
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Solution

## The correct option is A 60We need odd numbers which are greater than 8000 Two possible cases are there When the number is 4 digit Let the number be of the form ABCD A has to 8, so 1 way For D there are two choice 3,5, so 2 ways Now, there are 2 places and 3 numbers ∴ The number of ways =1×2×3×2=12 When the number is 5 digit Let the number be of form ABCDE For E there are two choice 3,5, so 2 ways Now, there are 4 places and 4 numbers ∴ The number of ways =4!×2=48 Hence, the total required numbers =12+48=60

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