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

495 different combinations of books are possible.

Step-by-step explanation

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

`_nC_r=(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=(n!)/(r!(n-r)!)=(12!)/(4!(12-4)!)=(12!)/(4!*8!)=(12*11*10*9*8!)/(4*3*2*8!)=495 \\ \\ \end{gathered}`

Hence, there are 495 different combinations of books are possible