Finite Math

At Sally's Salads, there is an all you can eat salad bar. You may choose one of 3 different lettuces, any number of 11 vegetable toppings, and at most one of 6 dressings. Suppose a salad is made at random following those rules. If the salad includes a lettuce choice, but not necessarily anything else, what is the probability that you get a salad with 4 vegie toppings and Ranch dressing?

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  1. number of ways to choose 1 of 3 salads
    = C(3,1) = 3
    number of ways to choose any number of 11 toppings, including choosing no topping
    = 2^11 = 2048

    number of possible salads = 3(2048) = 6144

    number of salads with Ranch and 4 dopping
    = 1x C(11,4) = 330

    prop of event = 330/6144
    = 55/1024

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