Question

A textbook search committee is considering 18 books for possible adoption. The committee has decided to select 5 of the 18 for further consideration. In how many ways can it do so?

Answer 1

In order to select 5 books from the 18 possible, we use combinations because the order, in this case, won't matter, this means that

$\text{abcde}=\text{cbaed}$

then, by definition

$\text{nCr}=\frac{n!}{r!(n-r)!}$

then,

$\begin{gathered} 18C5=\frac{18!}{5!13!} \\ 18C5=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5\cdot4\cdot3\cdot2\cdot1\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ 18C5=\frac{18\cdot17\cdot16\cdot15\cdot14}{5\cdot4\cdot3\cdot2\cdot1}=\frac{1028160}{120} \\ 18C5=8568 \end{gathered}$