Probability. We are randomly lining up 4 ranchers and 3 shepards, for a total of seven people.

What is the probability that the line will alternate between ranchers and shepards?

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 =

Hence, the probability that the line will alternate between ranchers and shepherds =  

5+2x=a

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the answer is 5/14.

hope this .