A person has 8 friends, of whom 5 will be invited to a party.(a) How many choices are there if 2 of the friends are feuding and will not attend together?(b) How many choices if 2 of the friends will only attend together?
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in number 20 he says that person has eight friends, of whom five will be invited to a party. So just information from this we have eight friends and five are invited to a party part A. How many choices are there if two of the friends refuting and will not attend together? So since two friends or feuding and they're not gonna be at the party together, we have to figure out this in stages. So let's assume that friend one is selected if friend one insulated, that eliminates friend too. Friend to is absolutely not coming. So we know that friend one is coming. So there's six possible selections remaining. This is a combination because the order in which they're selected doesn't matter. Um, and because friend one has been selected, there are four possibilities left. So out of six friends, we can invite four. Assuming that friend one is coming. That gives us 15 different selections. If you follow that same logic, if we assume friend to is coming, it's the same logic friend. One will not be coming so the other six friends can come in for are available to be invited. That also gives us 15, so option one could happen or option two could happen or option three or neither of these two come. If this were the option, then there would be six people that could be chosen for this combination and any other five or okay to come. This gives us six. So adding these three together we get 36 total possibilities with two friends feuding and refusing to come at the same time. Alright, NB B says How many choices if two of the friends will Onley attend together? So how many choices if two of their friends will only attend together? So this one is also done in stages? Um, let's assume that the two friends are selected. If the two friends were selected, then there are six other possibilities that could be selected. Um, but there's only three spots available, so six possibilities of three spots gives us 20 possibilities here. Um or we can assume that the two friends are not selected. If this is the case and this is true, there are six possibilities and all five spots are still available.
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This gives us six possibilities. We're gonna add those together because these were the only two ways they're either both coming or they're both not coming way have 26 possible ways if two friends will only come together.