Question

The total number of $5$ digit numbers of different digits in which the digit in the middle is the largest, is

• A. $32\left(5!\right)$
• B. $35\left(3!\right)$
• C. $32\left(3!\right)$
• D. None of these.

Answer 1

The correct option is D

None of these.

Formation of $5$-digit number:

Five digit number with digit in the middle is largest.

Thus five digit numbers$={}^{10}C_5\times 1!\times 4!$

$=6048$

If we include $0$ than number is no more $5$ digit number, it is $4$ digit number.

Thus, total numbers which includes $0$ $={}^{9}C_4\times 1\times 1\times 3!$

$=756$

Therefore total numbers of required condition $=6048-756$

$=5292$

Hence option (D) is the correct option.