Question

The total number of five-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. $33(3!)$
• C. $30(3!)$
• D. none of these

Answer 1

The correct option is D none of these

$\begin{array}{ccc}Middledigit& Digitsavailableforremainingfourplaces& Numberofwaysfillingremainingfourplaces\\ 4& 0,1,2,3& 3\times {}^3{P}_3\\ 5& 0,1,...,4& 4\times {}^4{P}_4\\ 6& 0,1,...,5& 5\times {}^5{P}_3\\ 7& 0,1,...,6& 6\times {}^6{P}_3\\ 8& 0,1,...,7& 7\times {}^7{P}_3\\ 9& 0,1,...,8& 8\times {}^8{P}_3\end{array}$