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What is the sum of all $5-$digit numbers possible using with the numbers $ 1,3,5,7,9$(Repetition is not allowed)?

$A)6666660$                                  $B)6666600$

$C)6666666$                                  $D)6666606$
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The sum of all ‘n’ digit numbers that can be formed by using all ‘n’ non-zero digits at a time

= $(n-1)!*(sum of the digits)*(1111...n times)$

$= (5-1)!*(1+3+5+7+9)*(11111)$

$= (24)*(25)*(11111)$

$= 6666600$

Hence, option B.

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