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

1.	In how many ways can six persons be seated in a row?
Answer» 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

Answer»

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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