One can also approach it as follows:

The first person has

7 persons to choose from to form a team with.

After the first pair has been formed, there are 6 more people in the group. The first person from this group of 6 will have

5 persons to choose from to form a team with.

Once the second pair is formed, there are 4 more people in the group. The first person in this group of 4 will have

3 persons to choose from to form a team.

Once the third pair is formed, only 2 more people are left with and they have only

1 choice.

Hence the total no. of pairs is 7*5*3*1 = 105

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Regards

Subhen