Question

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

Answer 1

Let us assume that there are six seats.

In the first seat, any one of six members can be seated, therefore the total number of possibilities is ⁶C₁

In the second seat, any one of five members can be seated, therefore the total number of possibilities is ⁵C₁ ways.

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

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

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

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

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