#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

my approach is first we select 1 person from 20,then for next we have only 18 choices(removing the one that is selected and his husband/wife) & same for remaining one!

(20*18*16*14*12)/20C5

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himgta YES! I guess it is the correct answer,Isn't it?

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himgta your approach is correct 

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@Mk Utkarsh

@Utkarsh Joshi

Answer given as (10C5*32)/20C5

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himgta YES answer given by them is correct. With the approach, u suggested we are even considering their order, but in this case we have to just select people not arrange. Divide your answer by 5! that's what they are saying.

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given ans  is correct

because, we can d it like this

Here 10 men and 10 women

1) Select 5 men from 10 men

2) Select 4 men from 10 men and 1 woman from 6 women

3) Select 3 men from 10 men and 2 woman from 7 women

and ..........

Now that will be $\binom{10}{5}+\binom{10}{4}\times \binom{6}{1}+\binom{10}{3}\times \binom{7}{2}+\binom{10}{2}\times \binom{8}{3}+\binom{10}{1}\times \binom{9}{4}+\binom{10}{5}=32\times \binom{10}{5}$

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@srestha mam

@Utkarsh Joshi 

what is wrong with my approach?

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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!