hey, i've been stuck on this question. i keep getting the answer 30.
In a tennis club, there are five married couples available to play a "mixed doubles" match, that is, a match in which a combination of one man and one woman play against a combination of another man and another woman. In haw many ways can a group of four persons be chosen for this match if:
(b) a man and his wife may not play in the match either as partners or as opponents.
Answer is 60
Hey Chloe!
Okay, so we have here a combinations question! I find the best way to do these is to separate into any separate categories, in this case, men and women. Doing that, let's proceed!
So let's say we choose the two males first. This would be a combination of 2 males from a possible 5, and so:
Now, we can pick their partners. Two of the women are not allowed to be chosen, because their husbands are in the game already. Therefore, we are selecting 2 women from 3 possible choices:
Now at this point, the answer of 30 becomes apparent:
Now, I was a little confused, and I think the wording of the question is poor here.
We haven't considered which team the women choose to join in the second step. That is, when we choose the women, they can join the teams in one way, or they can swap sides and join in another way. So, we multiply our final answer by 2:
Now, the question only said how many ways the groups can be chosen, which I suppose implicitly suggests that we consider different teams as well, but I'd totally forgive someone for not doing it, because technically, changing the teams does not change the group.
But yep, that's where the 60 comes from. Hope this helps Chloe!