Question

Find the average of all five digit numbers that can be formed using all the digits $1,2,3,4,5$ exactly once?

• A. $33453$
• B. $34333$
• C. $33333$
• D. None of these

Answer 1

The correct option is C $\left(33333\right)$

The given digits are $1,2,3,4,5$
The number of five digit numbers are $5!=5\times 4\times 3\times 2\times 1=120$
Since, each digit of $1,2,3,4$ and $5$ occur in every one of the five decimal places.
So, we will find average according to its place values and each place value sum gives the same number as the average of given numbers $1,2,3,4,5$.
Thus, the average of each decimal place$=\frac{(1+2+3+4+5)}{5}=3$.
So, the average of all $5$ digit no. is $3\times 10000+3\times 1000+3\times 100+3\times 10+3$
$30000+3000+300+30+3=33333$.