Question #0dedf

1 Answer
sente
Dec 12, 2016

#70#

Explanation:

Assuming the #8# objects are distinct, then this is equivalent to the number of ways of choosing #4# objects from the group of #8#, as if that is the first group, then the remaining #4# is decided as the second group.

The number of ways of choosing #k# objects from a set of #n# objects can be calculated as

#((n),(k)) = (n!)/(k!(n-k)!)#

(read as #n# choose #k#)

Applying this to the given question, we have the number of ways of choosing a set of #4# objects from a set of #8# as

#((8),(4)) = (8!)/(4!(8-4)!)#

#=(8*7*6*...*3*2*1)/((4*3*2*1)(4*3*2*1)#

#=(8*7*6*5)/(4*3*2*1)#

#=70#

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