Question

Suppose you choose four booksto read from a summer readinglist of 12 books. How manydifferent combinations of booksare possible?Note: nCrn!r!(n-r)!

Answer 1

Answer

495 different combinations of books are possible.

Explanation

The different combinations of books possible can be known using the given formula

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

Choosing four books to read from a list of 12 books means r = 4 and n = 12

Therefore

$\begin{gathered} _nC_r=\frac{n!}{r!(n-r)!}=\frac{12!}{4!(12-4)!}=\frac{12!}{4!\times8!}=\frac{12\times11\times10\times9\times8!}{4\times3\times2\times8!}=495 \\ \\ \end{gathered}$

Hence, there are 495 different combinations of books are possible