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}=(n!)/(r!(n-r)!)`

then,

`\begin{gathered} 18C5=(18!)/(5!13!) \\ 18C5=(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=(18\cdot17\cdot16\cdot15\cdot14)/(5\cdot4\cdot3\cdot2\cdot1)=(1028160)/(120) \\ 18C5=8568 \end{gathered}`