SOLUTION: Ten students are in pairs on a field trip. How many different pairs of students are possible?

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Question 732291: Ten students are in pairs on a field trip. How many different pairs of students are possible?
Found 3 solutions by lynnlo, Alan3354, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Ten students are in pairs on a field trip. How many different pairs of students are possible?
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The 1st chosen is 1 of 10, then 1 of 9
10*9 = 90

Answer by ikleyn(53418) About Me  (Show Source):
You can put this solution on YOUR website!
.
Ten students are in pairs on a field trip.
How many different pairs of students are possible?
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%2810%2A9%29%2F2 = 90%2F2 = 45 different ways to make pairs of 10 students are possible.

It is the number of combinations of 10 items taken 2 at a time.

The order in pairs does not matter, so we use combinations.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
    To better understand the problem, imagine 10 x 10 grid on graph paper.

    Each point in this grid represent one pair.

    The diagonal (10 points) should be excluded: 100 minus 10 gives 90,  100-10 = 90.


    The pints symmetric about the diagonal, represent the same pair.

    So, we divide 90 by 2 and get the same 45 what we need.


    It is the geometric interpretation for your better understanding.
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Solved.

The answer in the post by @lynnlo is incorrect.

Simply ignore his post.