Question

The total number of 5-digit numbers of different digits in which the digit in the middle is the largest is:

• A. $\sum _{n=4}^9{}^n{P}_4$
• B. $33\left(31\right)$
• C. $30\left(31\right)$
• D. none of these

Answer 1

The correct option is D none of these

Note that the digits of $5$ digit number are to be different.
$⟨||||⟩\uparrow largest$
Total number of such a number $=\left(\begin{array}{c}10\\ 5\end{array}\right)\times 1\times 4!-\left(\begin{array}{c}9\\ 4\end{array}\right)\times 1\times 1\times 3!=5292$
subtraction because if $0$ is chosen and comes in the $1st$ position then the number will no longer be of $5$ digit.
Hence answer is $D$