Question

How do you evaluate `((8), (5))` using Pascal's triangle?

Answer 1

`56`

Explanation:

`"by definition "((n),(r))=(n!)/(r!(n-r)!)`

`((8),(5))=(8!)/(5!(8-5)!)`

`=(8!)/(5!xx3!)=(8xx7xx6xxcancel(5!))/(cancel(5!)xx3!)`

`=(8xx7xxcancel(6))/cancel(3!)`

`=56`

Answer 2

`56`

Explanation:

`((8),(5))" represents 8th row , 5th column"`

From Pascal's triangle the entry in the 8th row / 5th column is

`((8),(5))=56`

`"8th row "rarr1 color(white)(x)8color(white)(x) 28color(white)(x) 56color(white)() color(white)(x)70color(white)(x)color(red)(56)color(white)(x)28color(white)(x)8color(white)(x)1`

`color(white)(xxxxxxxxxxxxxxxxxxx)uarr`

`color(white)(xxxxxxxxxxxxxxxxxx)"5th column"`