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Q.
The sum of $5$ digit numbers in which only odd digits occur without any repetition is
Permutations and Combinations
Solution:
The digits that make the numbers are $1, 3, 5, 7$ and $9$.
The number of numbers with one of these in the first place $= 4!$.
$\therefore $ The required sum of all the numbers
$= 25\left(10^{4} + 10^{3} +10^{2} + 10 + 1\right)\times 4! $
$= 600 \times\frac{ 10^{5} -1}{10 -1 }$
$= 600 \times 11111$
$= 6666600$.