Sum of unit digit of all the number formed by given n different digit

Given : n different digit
i.e a1 , a2 , a3 .....................................an

Total Number having unit digit an = (n-1) !

Sum of unit digit of all the number having unit digit an = an (n - 1) !

Sum of unit digit of all the number formed =

  =   a1 (n -  1) !  +  a2(n  - 1) !      +    ...    +   an  (n  -1 ) !

  =     (a1   +   a2   +  .......    +   an )  (n  -  1) !

  =  (Sum   of   digits) (n  -1) !

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$