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  4. The sum of all 4 digit numbers that can be formed by using the digits 2, 4, 6, 8 (repetition of digits not allowed) is

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Q. The sum of all $4$ digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

Permutations and Combinations

Solution:

There are $4! = 24$ numbers. Each digit occurring $3! = 6$ times, in the unit's, ten's, hundred’s and thousand's places. We note that $6(2 + 4 + 6 + 8) = 120$. Thus in the over all sum there will be $120$ units, $120$ tens, $120$ hundreds and $120$ thousands.
$\therefore $ The required sum $= 120 (1 + 10 + 10^2 + 10^3)$
$ = 120 \times 1111 = 133320$.