a box contains 3 pairs of blue gloves and two pairs of green gloves . each pair consists of a left - hand glove and a right - hand glove . each of the gloves is separate from its mate and thoroughly mixed together with the others in the box . if 3 gloves are randomly selected from the box , what is the probability that a matched set ( i . e . , a left - and right - hand glove of the same color ) will be among the 3 gloves selected ? Choose the correct answer:
A) 3 / 10	B) 23 / 60	C) 7 / 12	D) 41 / 60	E) 5 / 6

Rationale: you can use the ' calculating the reverse ' method used by bunuel above or if you would like to calculate the probability of getting a matched set in the usual way , you can think of it in this way : bleft ( 3 ) , bright ( 3 ) , gleft ( 2 ) , gright ( 2 ) bleft , bright , g get a bleft and bright in ( 3 / 10 ) * ( 3 / 9 ) ways . then get any green in 4 / 8 ways . probability of getting b pair and a g = ( 3 / 10 ) * ( 3 / 9 ) * ( 4 / 8 ) * 3 ! ( you multiply by 3 ! here because you could pick in some other order e . g . bright , bleft , g or bleft , g , bright etc ) bleft , bright , b get a bleft and bright in ( 3 / 10 ) * ( 3 / 9 ) ways . then get any blue in 4 / 8 ways . probability of getting b pair and another b = ( 3 / 10 ) * ( 3 / 9 ) * ( 4 / 8 ) * 3 ! / 2 ! ( you multiply by 3 ! here to account for the order e . g . bright , bleft , bleft or bleft , bright , bright etc but two gloves will be identical so you divide by 2 ! ) gleft , gright , b get a gleft and gright in ( 2 / 10 ) * ( 2 / 9 ) ways . then get any blue in 6 / 8 ways . probability of getting g pair and a b = ( 2 / 10 ) * ( 2 / 9 ) * ( 6 / 8 ) * 3 ! gleft , gright , g get a gleft and gright in ( 2 / 10 ) * ( 2 / 9 ) ways . then get any other g in 2 / 8 ways . probability of getting g pair and a g = ( 2 / 10 ) * ( 2 / 9 ) * ( 2 / 8 ) * 3 ! / 2 ! adding them all up , you get 41 / 60 . answer : d
Answer: D