A cupboard contains 8 pairs of shoes, each of a different style. How many ways are there to select 6 pairs of the shoes from the cupboard so that the selection contains exactly 2 pairs. Note that each pair of shoes consists of a distinguishable left and right foot.

Question

anonymous · Answer

HELP!!!

raden · Answer

i dont understand of  "contains exactly 2 pairs" ?

anonymous · Answer

As in a left and a right of a pair of Nike Airs and and a left and a right of a pair of Adiddas. The other 2 shoes must be unpaired (e.g. a left from a Rebok and a left/right  from Mizuno)

raden · Answer

ok. i see..
it is a combination problem (sorry i was lola, my english so bad)
so, just use formula :
nCr = n!/((n-r)!*r!)
put n=8 and r=6 to formula above

raden · Answer

do u know factorial ?

anonymous · Answer

for selection by random, we can get :
8C6= 8!/((8-6)!6! = 28 ways
and next for selection contains exactly 2 pairs, it similar means how to selection 2 pairs contains exactly from 28 selected, so use permutation get : (permutation of with same unsur/elements)
P=28!/2!