Question

Determine the average of all four digit numbers that can be made using all the digits $2,3,5,7$ and $8$ exactly once?

• A. $3993$
• B. $5555$
• C. $5486$
• D. $5347$

Answer 1

The correct option is B $5555$

First we need to find the sum of all possible numbers and then divide it by the total such numbers possible to gain an average of all the numbers.
Total numbers that can be formed $={}^5{P}_4$
and each digit get repeated $24$ times on each place
Hence sum of all such digits
$=24(8+2+3+5+7)(1+10+100+1000)=24\times 25\times 1111$
Hence, the average will be $=5555$