anonymous
  • anonymous
A box contains six red, three green, and four blue balls. In how many ways is it possible to select a sample of four balls, without replacement, in which at most three are red?
Mathematics
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anonymous
  • anonymous
A box contains six red, three green, and four blue balls. In how many ways is it possible to select a sample of four balls, without replacement, in which at most three are red?
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
You have to pick four balls, and *at most* three are red, then I would consider the case of selecting more than three - i.e. four red balls - as the number of cases you *don't* want, and subtract this from the number of total cases available. (# ways to select 4 balls without replacement in which at most 3 are red ) = (# ways to pick any 4 balls) - (# ways to pick 4 red balls) = 13 x 12 x 11 x 10 - 4 x 3 x 2 x 1 =17136

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