SOLUTION: in how many different ways can two students be selected from among a group of five students? How does this compare with the number of way that three students could be selected from

C(5,2) = 10
If the students are {A,B,C,D,E}, those 10 ways are
{A,B}, {A,C}, {A,D}, {A,E}, {B,C}, {B,D}, {B,E}, {C,D}, {C,E}, {D,E}

C(5,3) = 10

They are the same and the reason they are is
 
1. every time you pick 2 student from the 5 you are automatically picking 3 students to leave behind. 

and vice-versa,

2. every time you pick 3 student from the 5 you are automatically picking 2 students to leave behind.

So they have to be the same.

If the students are {A,B,C,D,E}, those 10 ways are

{A,B,C}, {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E},
{A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, {C,D,E}

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So in general, C(n,r) = C(n,n-r)

Edwin