Question 732291
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Ten students are in pairs on a field trip.  
How many different pairs of students are possible?
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{{{(10*9)/2}}} = {{{90/2}}} = 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.


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<pre>
    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.
</pre>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Solved.


The answer in the post by @lynnlo is incorrect.  


Simply ignore his post.