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The sum of all five digit numbers that can be formed using the

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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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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).

5 mins ago

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5 mins ago

Text solutionVerified

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 \times 4! (5 + 4 + 3 + 2 + 1)

Similarly, for hundred's, thousand's and ten thousand's place the sum are

1 0^{2} \times 4! (5 + 4 + 3 + 2 + 1), 1 0^{3} \times 4! (5 + 4 + 3 + 2 + 1), 1 0^{4} \times 4! (5 + 4 + 3 + 2 + 1)

respectively.

Hence, the required sum

= (4)! (1 + 2 + 3 + 4 + 5) (1 + 10 + 1 0^{2} + 1 0^{3} + 1 0^{4})

= 24 \times 15 \times (\frac{1 0 ^{5} - 1}{10 - 1})

= 24 \times 15 \times 11111

= 3999960

The first digit is

3

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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).

Text solutionVerified

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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).