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

Solution:

Assume there are six seats available.

Any one of six members can sit in the first seat, bringing the total number of options to ⁶C₁.

The second seat can be occupied by any of the five members, resulting in a total of ⁵C₁  options.

The third seat can be occupied by any of the four members, giving a total of  ⁴C₁ options.

Any of the three members can sit in the fourth seat, bringing the total number of possibilities to ³C₁.

Any one of two members can sit in the fifth seat, resulting in a total of ²C₁ possibilities.

Only one more person can sit in the sixth seat, bringing the total number of options to ¹C₁.

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