withoutaface
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8C4/2<sup>8</sup>
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pLuvia
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i dont understand 
Sorry, I should have given some sort of explanation.
In order to work out the total number of ways that one can arrange 8 people into two groups you should consider each individual person and let the two groups be group A and group B. For each person there are two options: either they go into group A or they go into group B. If you drew a tree diagram of this each branch would become two branches (since you have 2 options at each decision point where a person is put into A or B). This gives you:
2x2x...x2 = 2<sup>8</sup> ways , but you have to subtract the cases where all 8 people are in group A or all 8 are in group B so the number of ways to divide 8 people between two groups is (2<sup>8</sup> - 2)
When working out the number of ways to split the people into 2 groups of 4 it's probably easier to think about the selection of only one group. I'm sure that you agree that the number of ways you can make a group of 4 from 8 people is <sup>8</sup>C<sub>4</sub>. What you'll realise if you think about it is that for every group you have selected, the group that you have left behind is also a group of 4 and that as your selected group cycles through every possible option so does the group that is left behind.
The answer you end up with is: <sup>8</sup>C<sub>4</sub>/(2<sup>8</sup> - 2)
In order to work out the total number of ways that one can arrange 8 people into two groups you should consider each individual person and let the two groups be group A and group B. For each person there are two options: either they go into group A or they go into group B. If you drew a tree diagram of this each branch would become two branches (since you have 2 options at each decision point where a person is put into A or B). This gives you:
2x2x...x2 = 2<sup>8</sup> ways , but you have to subtract the cases where all 8 people are in group A or all 8 are in group B so the number of ways to divide 8 people between two groups is (2<sup>8</sup> - 2)
When working out the number of ways to split the people into 2 groups of 4 it's probably easier to think about the selection of only one group. I'm sure that you agree that the number of ways you can make a group of 4 from 8 people is <sup>8</sup>C<sub>4</sub>. What you'll realise if you think about it is that for every group you have selected, the group that you have left behind is also a group of 4 and that as your selected group cycles through every possible option so does the group that is left behind.
The answer you end up with is: <sup>8</sup>C<sub>4</sub>/(2<sup>8</sup> - 2)
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