Question

Pablo randomly picks three marbles from a bag of seven marbles (four red ones, two green ones, and one yellow one).

How many outcomes are there in the sample space?
How many outcomes are there in the event that all of the marbles he picks are red?

Answer 1

• 35
• 4

Explanation:

You want to know the number of outcomes in the sample space when 3 marbles are chosen from 7. If four are red marbles, you want to know the number of outcomes when all chosen are red.

Outcomes

There are C(7,3) = 7!/(4!·3!) = 35 ways to choose 3 marbles from 7. Given that there are different colored marbles involved, not all of these outcomes are unique.

There are 35 possible outcomes.

3 Red

There are C(4, 3) = 4 ways to choose 3 red marbles from 4 red marbles.

There are 4 possible outcomes with all red marbles.

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Additional comment

The 35 possible outcomes are ...

(RRR) - 4, (RRG) - 12, (RRY) - 6, (RGG) - 4, (RGY) - 8, (GGY) - 1

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