Answer: [tex]\dfrac{1}{35}[/tex]
Step-by-step explanation:
Given: We need to line up 4 ranchers and 3 shepherds, for a total of seven people.
i.e. we are placing all of them , so we have 4 places for ranchers and 3 places for shepherds between them.
Number of ways to line up alternate between ranchers and shepherds = 4! x 3!
= 24 x 6
= 144
Total number of ways to line up 7 persons = 7! = 5040
Required probability = [tex]\dfrac{144}{5040}=\dfrac{1}{35}[/tex]
Hence, the probability that the line will alternate between ranchers and shepherds = [tex]\dfrac{1}{35}[/tex]
