In how many ways can six persons be seated in a row?

Given: Six persons are to be arranged in a row


Assume six seats, now in the first seat, any one of six members can be seated, so the total number of possibilities is 6C1


Similarly, in the second seat, any one of five members can be seated, so the total number of possibilities is 5C1


In the third seat, any one of four members can be seated, so the total number of possibilities is 4C1


In the fourth seat, any one of three members can be seated, so the total number of possibilities is 3C1


In the fifth seat, any one of two members can be seated, so the total number of possibilities is 2C1


In the sixth seat, only one remaining person can be seated, so the total number of possibilities is 1C1


Hence the total number of possible outcomes = 6C1 × 5C1 × 4C1 × 3C1 × 2C1 × 1C1 = 6 × 5 × 4 × 3 × 2 × 1 = 720


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