Discussing orderless choice of two items from n items

Orderless choice of 2 objects from n objects

We know that the number of ways of choosing two items from n items is given by $^nC_2$
We can look at the choice problem as in the diagram below.

Each node in the tree is representative of a choice of two items. Therefore total number of choices is equal to the number of nodes in the above tree. Total number of nodes is
$1+2+3+4......(n-1)$ = $\frac{n(n-1)}{2}$ = $^nC_2$
Similar analysis and derivation could be done for $^nC_3$ and $^nC_r$



RP
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