The sum of all five digit numbers that can be formed using the digits 1,2,3,4 and 5 is found.The first digit is (repetition of digits not allowed).

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Filo · Accepted Answer

If 5 is at the unit's place, the remaining digits 1,2,3 and 4 can be arranged among themselves in 4! ways. Hence, there are exactly 4! five-digit numbers using the given digits.Similarly, there are exactly 4! five-digit numbers using the given digits. Similarly for other digits.Hence the total sum of digits at unit's place for all numbers possible is 4!(5+4+3+2+1)Similarly, the total sum of digits at ten's place for all numbers possible is 10×4!(5+4+3+2+1)Similarly, for hundred's, thousand's and ten thousand's place the sum are 102×4!(5+4+3+2+1),103×4!(5+4+3+2+1),104×4!(5+4+3+2+1) respectively.Hence, the required sum= (4)!(1+2+3+4+5)(1+10+102+103+104 )=24×15×(10−1105−1​)=24×15×11111=3999960The first digit is 3.

Question Text	The sum of all five digit numbers that can be formed using the digits $1, 2, 3, 4$ and $5$ is found.The first digit is (repetition of digits not allowed).
Answer Type	Text solution:1
Upvotes	151

The sum of all five digit numbers that can be formed using the digits $1, 2, 3, 4$ and $5$ is found.The first digit is (repetition of digits not allowed).

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