Question

You have spent a very long time training your dog to open the refrigerator and bring you a drink when you ask him to. Since your pet can’t read, his selection of the specific type of beverage he brings is completely random – although you notice that, for reasons beyond your understanding, and aside from whatever else he brings, he always brings you 2 (and only 2) grapefruit juices on any given day. One particular day, you ask your pet to bring you 4 drinks. You know that there are 6 bottles of orange juice, 4 bottles of grapefruit juice, and 3 bottles of apple juice in your fridge. Of all the possible combinations of types of drinks that your dog could select, what proportion of those combinations will contain the requisite 2 bottles of grapefruit juice that you know he will inevitably bring?