# How do combinations relate to the pascal's triangle?

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

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

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

4th row has 1 4 6 4 1 elements, that is ${4}_{C} 0$, ${4}_{C} 1$, ${4}_{C} 2$, ${4}_{C} 3$, ${4}_{C} 4$

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