A box contains three 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 three 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 three gloves selected?
Choose the correct answer:
A) 3/10	B) 23/60	C) 7/12	D) 41/60	E) 5/6
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:41/60
<result>D</result>
A box contains three 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 three 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 three gloves selected?