# In how many ways can you arrange six out of eight books on a shelf?

Mar 16, 2016

I hope I am correct! 28 ways

#### Explanation:

This is a permutation question

The number of arrangements is (n!)/((n-r)!r!)

where
$n = 8$
$r = 6$

Giving
color(brown)((n!)/((n-r)!r!))" "->" " color(blue)(( 8!)/((8-6)!6!)

Always look for factorials that can be cancelled.

" "(8xx7xxcancel(6!))/((2xx1)xxcancel(6!) )

$\text{ } 4 \times 7 = 28$