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How do combinations relate to the pascal's triangle?

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Apr 6, 2015

In the pascal's triangle the row wise elements are as follows:

1st row has one element 1, that is $1_{C}$ $1_C$ 1

2nd row has 3 elements 1 2 1, that is $2_{C}$ $2_C$ 0, $2_{C}$ $2_C$ 1, $2_{C}$ $2_C$ 2

3rd row has 4 elements 1 3 3 1, that is $3_{C}$ $3_C$ 0, $3_{C}$ $3_C$ 1,
$3_{C} 2$ $3_C2$ , $3_{C}$ $3_C$ 3

4th row has 1 4 6 4 1 elements, that is $4_{C} 0$ $4_C0$ , $4_{C} 1$ $4_C1$ , $4_{C} 2$ $4_C2$ , $4_{C} 3$ $4_C3$ , $4_{C} 4$ $4_C4$

This pattern is then followed through out, showing, how combinations relate to pascal's triangle

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