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. $8888$

Answer 1

The correct option is C

$6666$

Explanation of the correct option:

Finding the average of four-digit numbers:

The average of a list of numbers is equal to the ratio of the sum of all the numbers and the number of numbers. Given, here $3,5,7$and $9$ are the digits.

Total $4$ digit numbers that can be formed

$\begin{array}{rcl}n& =& 4!\\ & =& 24\end{array}$

Therefore, all digits will appear exactly the same number of times.

$$\begin{gathered} \mathrm{Average}\mathrm{of}\mathrm{numbers}=\frac{3!(3+5+7+9)\times 1111}{4!} \\ =\frac{6\times 24\times 1111}{24} \\ =\frac{6\times 1111}{1} \\ =6666 \end{gathered}$$

Therefore, the correct answer is option (C).