Question

1. A box contains 3 left-handed gloves and 5 right-handed gloves. If we randomly select 3 gloves from the box, what is the probability that we obtain a useable pair of gloves? That is, what is the probability that we obtain at least one left-handed glove and at least one right-handed glove?
   1. 1/56
   2. 10/56
   3. 45/56
   4. 11/56
   5. 13/56

Answer 1

Total gloves = 3 + 5 = 8

Total number of ways to select 3 gloves = 8C3 = 8! / (3! * (8 - 3)!) = 56

Total number of ways to select at least one left handed and at least one right handed glove = Total number of ways to select one left handed and two right handed gloves + Total number of ways to select two left handed and one right handed gloves

                                                                  = 3C1 * 5C2 + 3C2 * 5C1

                                                                  = 3 * 10 + 3 * 5

                                                                  = 45

P(at least one left handed and at least one right handed glove) = 45 / 56

Option-C) 45/56