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. $24$
• B. $12$
• C. $65$
• D. $60$

Answer 1

The correct option is D $60$

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
$\therefore$ The number of ways
$=1\times 2\times 3\times 2=12$

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
$\therefore$ The number of ways
$=4!\times 2=48$

Hence, the total required numbers $=12+48=60$