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In 8*7*6*5*4*3 = 20160 different ways.
1-st person can take any of 8 chairs. - 8 possibilities.
2-nd person can take any of remaining 7 chairs. - 7 possibilities.
3-rd person can take any of remaining 6 chairs. - 6 possibilities.
. . . . And so on . . . .
6-th person can take any of remaining 3 chairs. - 3 possibilities.
Thus there are 8*7*6*5*4*3 = 20160 different ways.