Question

A textbook search committee is considering 17 books for possible adoption. The committee has decided

select 8 of the 17 for further consideration. In how many ways can it do so?

Answer 1

Given,

The number of books considered for possible adaptation is 17.

The number of books to be select is 8.

The number of ways books can be selected is calculated as,

`^nC_r`

Here, n is the number of total books.

r is the number of books to select.

Substituting the values of n and r then,

`\begin{gathered} ^(17)C_8=(17!)/((17-8)!8!) \\ =(17!)/(9!8!) \\ =(17*16*15*14*13*12*11*10*9!)/(9!*8*7*6*5*4*3*2*1) \\ =17*5*13*2*11 \\ =85*13*22 \\ =85*286 \\ =24310 \end{gathered}`

Hence, the number of ways books can be selected is 24310.