SOLUTION: A bag contains three red marbles, two green ones, one lavender one, two yellows, and three orange marbles. How many sets of five marbles include at least two red ones? sets

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Question 1113772: A bag contains three red marbles, two green ones, one lavender one, two yellows, and three orange marbles.
How many sets of five marbles include at least two red ones?
sets
Answer by greenestamps(13198) About Me  (Show Source):
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There are 3 red marbles and 8 others. You are making sets of either 2 of the 3 red and 3 of the 8 others, or all 3 of the red and 2 of the 8 others:

"3 choose 2" times "8 choose 3" plus "3 choose 3" times "8 choose 2"

(3C2)*(8C3)+(3C3)(8C2) = 3*56+1*28 = 168+28 = 196