SOLUTION: 8.) A bag contains fourteen yellow balls, two violet balls, and nine red balls. You pick one without looking. What is the probability that you will draw three red balls in a row?

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Question 999875: 8.) A bag contains fourteen yellow balls, two violet balls, and nine red balls. You pick one without looking. What is the probability that you will draw three red balls in a row?
Answer by ikleyn(52814) About Me  (Show Source):
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8.)  A bag contains fourteen yellow balls, two violet balls, and nine red balls.  You pick one without looking.
What is the probability that you will draw three red balls in a row?
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14 + 2 + 9 = 25.

The solution below assumes that you pick up the balls one after one and do not return them back.

The full space of events consists of combinations of  25  things taken  3  at a time;  i.e.  C%5B25%5D%5E3  combinations.
Of them three red balls in a row you can choose by  C%5B9%5D%5E3 ways.

Hence,  the probability is

C%5B9%5D%5E3 : C%5B25%5D%5E3 = %289%2A8%2A7%29%2F%281%2A2%2A3%29 : %2825%2A24%2A23%29%2F%281%2A2%2A3%29 = %289%2A8%2A7%29%2F%2825%2A24%2A23%29 = %283%2A7%29%2F%2825%2A23%29 = 0.036522 (approximately).