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## Homework Statement

There are 20 couples who attend a party where there is a raffle. 10 Winners are chosen in the raffle. What is the expected number of couples for which both members win.

## Homework Equations

Assuming method of indicators is used to solve the problem, A

_{i}={members of i

^{th}couple win}.

## The Attempt at a Solution

The Expected value would be the sum of all P(A

_{i}), or 20P(A

_{i}), correct?

I'm having a little trouble figuring out what P(A

_{i}) would be though. If there are 20 couples, then there are 40 people. So the total number of outcomes for winners is 40nCr10, right? I'm not quite sure what the numerator would be in this instance however... Then I thought just going through straight numerical probability, the probability of one person winning would be 10/40, and their counterpart winning would then be 1/39, so P(A

_{i})=10/(40*39)? I still feel as though that is incorrect however.

Any insight you all could provide would be very helpful! Thank you!