Question

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

Answer 1

Step-by-step explanation:

Total number of books = 12

n = 12

amount to be chosen = 4

r = 4

To determine the different combination of books possible, we will use the combination formula:

`^nC_r\text{ = }\frac{n!}{r!(n\text{ - r)!}}`

substitute the values:

`\begin{gathered} ^(12)C_4\text{ = }\frac{12!}{4!(12\text{ - 4)!}} \\ ^(12)C_4\text{ = }\frac{12!}{4!8\text{!}} \\ =\text{ }\frac{12*11*10*9*8!}{4!*8\text{!}} \\ =\text{ }(12*11*10*9)/(4!)\text{ } \\ =\text{ }(12*11*10*9)/(4*3*2*1)\text{ } \\ \\ ^(12)C_4\text{ }=\text{ }495 \end{gathered}`

495 different combination of books is possible