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