Question

Refer to Pascal's Triangle. Draw a circle around the element denoted by:

Answer 1

'6 choose 4' is how it's read

`\left(\begin{array}{ccc}n\\k\end{array}\right)`=
`(n!)/(k!(n-k)!)`
so


`\left(\begin{array}{ccc}6\\4\end{array}\right)`=
`(6!)/(4!(6-4)!)`=
`(720)/(24(2)!)`=
`(720)/(48)`=15

that means the coeficient of the 5th term is 15


or remember that


`\left(\begin{array}{ccc}n\\k\end{array}\right)` is for a binomial to the nth power, to find the k+1 term
so
4+1=5
look at row coresponding to 6th power (7th row from top)
cound 5 from left to right
get 15
15(a)^1(b)^5 is 5th term in binomial (a+b)^6