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  4. 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

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Q. 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

KEAMKEAM 2008Statistics

Solution:

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 $