call from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, two green ones, four white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]
She does not have all the red ones

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  1. 3 red
    2 green
    4 white
    2 purple ---> total = 11

    let's do the prob that she had the 3 reds
    number of such choices = C(3,3) x C(8,5) = 56
    number of choices of 8 from 11 = C(11,8) = 165

    prob(all 3 reds) = 56/165

    so prob(not all the reds) = 1 - 56/165 =109/165

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