X and y stand in a line with 6 other people . What is the probability that there are 3 persons between them
Answers
The total number of people including X and Y is 8. Those 8 can be arranged in 8! ways = 40320 ways.
So we need 3 people to be between X and Y. So we need to choose 3 people out of 6; because we excluded X and Y. Therefore, the number of ordered ways to choose 3 people out of 6 is 6P3=120 ways.
If we consider X, Y and the three people between them as one entity, we need to see how we can arrange this entity along with the 3 remaining people. Therefore, they can be arranged in 4! = 24 ways. One last thing, the X and Y can also be interchanged as Y and X. Therefore, X and Y can be arranged in 2 ways. We can conclude from all of this that the number of ordered ways we can place 3 people between X and Y is 120*24*2 = 5760 ways.
Therefore, probability will be 5760/40320 = 1/7.
Step-by-step explanation:
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