Another one from GMATClub Math Book's Probability chapter.

Given that there are 5 married couples. If we select only 3 people out of 10, what is the probability that none of them are married to each other?

They have given 3 different ways to solve it. All have gone over my head. Help!

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According to me(ATM):

Each time we select one person from the group of 10 people we are left with an two less no. of elegible people left to select from.

For example you and I form one couple then Kari and Sid form another and Rohu and Nammu form a third and so on, suppose Sakshi is doing the selection for us:

1. She will select one person at a time

2. In her first selection she picks you, so you were one of the 10C1 options she had.

3. Please note here, that once she picks you I am out of the running.

4. Now suppose in the second round of selection she picks Rohu, so that puts Nammu out of the running as well. So Rohu was 1 of the 8C1 options she had.

5. Lastly she pick Sid and puts Kari out. Sid was one of the 6C1 options she had.

This much was the selection part, now for probability we'll find all the cases without any restrictions, on couples or anything else, i.e., Sakshi can pick 3 people out of 10 in 10C3 ways.

Probability

=(Cases fulfilling criteria)/(Total no. of cases)

=(10C1*8C1*6C1)/(10C3)

=2/3

PS: I hope the answer is correct, otherwise "kela" will happen!

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