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$1! = 1$ .

$2! = 2$ .

$3! = 6$ .

$4! = 24$ .

$5!=120$ .

$6! = 720$ .

$5!$ is $120$ . So, the remaining factorials will all have their last digit as $0$ .

$1 + 2 + 6 + 24 = 33$ .

So the last digit of the expression is 3.

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