Answer:
[tex]Pr = \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]n = 4[/tex]
Required
Probability that you seat on the far left
First, we calculate the total possible seat arrangements.
This is calculated using:
[tex]Total =n![/tex]
[tex]Total =4![/tex]
[tex]Total =4*3*2*1[/tex]
[tex]Total =24[/tex]
Next, the possible seat arrangements if you seat at the far left.
This implies that you can only seat 1 spot while your friends (3) can seat on any of the remaining 3 seats.
i.e.
[tex]You \to 1[/tex]
[tex]Friend\ 1,2,3 \to 3,2,1[/tex]
The number of arrangement is:
[tex]Arrangement = 1 * 3 *2 *1[/tex]
[tex]Arrangement = 6[/tex]
The required probability is:
[tex]Pr = \frac{Arrangement}{Total}[/tex]
[tex]Pr = \frac{6}{24}[/tex]
Simplify
[tex]Pr = \frac{1}{4}[/tex]
