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(A) The total number of $4$ digit numbers that can be formed using $4$ distinct digits is $4! = 24$.Each digit appears in each place (units,tens,hundr

Vedclass · Accepted Answer

$133320$

Vedclass · Answer

(A) The total number of $4$ digit numbers that can be formed using $4$ distinct digits is $4! = 24$.Each digit appears in each place (units,tens,hundreds,thousands) an equal number of times,which is $24 / 4 = 6$ times.The sum of the given digits is $2 + 4 + 6 + 8 = 20$.The sum of the digits in any given place is $6 	imes 20 = 120$.Therefore,the sum of all such numbers is $120 	imes 1 + 120 	imes 10 + 120 	imes 100 + 120 	imes 1000$.$= 120(1 + 10 + 100 + 1000) = 120 	imes 1111 = 133320$.

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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