Question

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

• A. $4444$
• B. $5555$
• C. $6666$
• D. $7777$

Answer 1

The correct option is C

$6666$

Explanation for the correct option:

Step 1: Find the total number of digits formed from the four digits:

Estimate the number of ways that can be formed from the four digits.

The total numbers that can be formed

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

Step 2: Find the sum of all the numbers:

Estimate the sum using the fact that the number of times each digit appears will be the same.

$\begin{array}{rcl}S& =& 3!\left(3+5+7+9\right)\times 1111\\ & =& 159984\end{array}$

Step 3: Find the average of four digits numbers:

Find the average by dividing the sum by total numbers.

$\begin{array}{rcl}A& =& \frac{159984}{24}\\ & =& 6666\end{array}$

Hence, option (C) is correct.