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Question

How many four-digit odd numbers can be formed using the digits 0,2,3,5,6,8 (each digit occurs only once)?

A
64
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B
72
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C
86
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D
96
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Solution

The correct option is D 96
The digits from which we can choose digits is 0,2,3,5,6,8, that is a total of 6 digits
Since each desired number has to be odd , we must have any of 3,5 at the units place. This can be done in 2 ways
Also 0 has to occupy only the tens or the hundreds place, else the number would not be a 4 digit number. This can be done in 2 ways.
Now, the thousands, hundred's , tens digit can be formed by any of the digits 2,6,8, and one of 3 or 5, that is by 4 digits in 4P3=4!(43)!=4!1!=4×3×2=24 ways
So, total number of 4 digit odd numbers that can be formed =24×2×2=96 ways

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