Question

How many numbers greater than $24000$can be formed by using digits $1,2,3,4,5$when no digit is repeated?

• A. $36$
• B. $60$
• C. $84$
• D. $120$

Answer 1

The correct option is C

$84$

Explanation for the correct option:

To find the total numbers.

The given digits are $1,2,3,4,5$i.e. total $5$digits.

We have to find numbers greater than$24000$. Therefore, we will exclude the numbers starting with $1,21$and $23$

Now, numbers starting with $1$,has one digit fixed, and numbers starting with $21$and$23$ have two-digit fixed.

Thus required numbers$=$(Total) - (Those beginning with $1$) - (Those beginning with $21$) - (Those beginning with $23$)

$=5!-4!-3!-3!$

$$\begin{gathered} =120-24-6-6 \\ =84 \end{gathered}$$

Hence, the correct option is C.