#Sheldon ross example

Question

suppose 5 people are to be randomly selected from a group of 20 individuals
consisting of 10 married couples, and we want to determine P(N), the probability
that the 5 chosen are all unrelated. (That is, no two are married to each other.)?

Comments

As i said you are counting permutations which is not required.

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According to your approach, ABCDE and BACDE are different but we just want the number of selections and not permutations.

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Thanks @Utkarsh Joshi brother!