Question

The average of the four-digit numbers that can be formed using each of the digits $3,5,7$ and $9$ exactly once in each number is

• A. 4444
• B. 5555
• C. 6666
• D. 7777
• E. 8888

Answer 1

Answer: (C)

The sum of all the four digit numbers using the digits 3, 5, 7 and 9
$=(3+5+7+9)\times (4-1)!\left(\frac{{10}^4-1}{10-1}\right)$
$=24\times 6\times \left(\frac{{10}^4-1}{10-1}\right)=\frac{24\times 6\times 9999}{9}$
$\therefore$ Required average
$=\frac{24\times 6\times 9999}{9\times 24}=6666$