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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 60
We 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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