# How many different two-person teams can be made from 6 people?

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Feb 18, 2016

A 2 person team can be chosen in one of fifteen ways.

#### Explanation:

The question is not precise because if you treated it literally the answer would be 3. First you choose one team, 4 people are left in the group, the second team takes another 2 people and the remaining create the third team.

But I assume that the question is like "In how many ways a 2 people team can be chosen from 6 people?"

Such question has an answer $15$ because first member is chosen from 6 people (so there are 6 possibilities), the second person is chosen from remaining five people so the number is $6 \cdot 5 = 30$, but you have to divide the result by 2 because 2 people can be chosen in 2 ways but they still form the same team. It does not matter if you choose Ann first then John or the other way John first then Ann they form the same team.

There is also another way of calculating the number. A team of 2 chosen from six people is (in mathematics) a 2 element combination of a six element set.
The number of such combinations can be calculated as:

C""_6^2=((6),(2))=(6!)/(4!2!)=(1*2*3*4*5*6)/(1*2*3*4*1*2)=15

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