Question

Use Pascal's triangle to find 6C3

Answer 1

ignore tht pascal triangle its way too inefficient
Formula nCr = n! /r! (n-r)!
So 6C3= 6!/3!(6-3)!=20

Answer 2

Using Pascal's triangle

Number of terms Expression

1 = 1----------------------------
`(x+a)^0`

2 = 1 1----------------------------(x+a)

3 = 1 2 1-----------
`(x+a)^2`

4= 1 3 3 1----------
`(x+a)^3`

5= 1 4 6 4 1----------
`(x+a)^4`

6= 1 5 10 10 5 1----------
`(x+a)^5`

7= 1 6 15 20 15 6 1 ----------
`(x+a)^6`

8= 1 7 21 35 35 21 7 1 ----------
`(x+a)^7`

The meaning of
`_(3)^(6)\textrm{C}` , is coefficient of fourth term of an expression having 7 terms.

Using pascal Triangle value or coefficient of Fourth term of the expression

`(x+a)^6=\\\\\text{will be}\\\\_(3)^(6)\textrm{C}=20`