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

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Question 1148400: A bag contains three red marbles, one green one, one lavender one, two yellows, and three orange marbles.
How many sets of five marbles include at most one of the yellow ones?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Think of the types of marbles as being either "yellow marbles" or "non-yellow marbles". Therefore, there are:

2 yellow marbles
8 non-yellow marbles

"At most one of the yellow ones" means either 0 yellow marbles and 5 non-yellow marbles OR 1 yellow marble and 4 non-yellow marbles.

Ways to choose 0 yellow marbles and 5 non-yellow marbles: 8C5 = 8%21%2F%285%21%2A3%21%29 = 56

Ways to choose 1 yellow marble and 4 non-yellow marbles: 2C1 * 8C4 = %282%21%2F%281%21%2A1%21%29%29%2A+%288%21%2F%284%21%2A4%21%29%29 = 2 * 70 = 140

Ways to choose "at most one of the yellow ones" = 56 + 140 = 196