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Probability- Gravner -17.b

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A bag contains $80$ balls numbered {1, . . . , 80}. Before the game starts, you choose $10$ different numbers from among {1, . . . , 80} and write them on a piece of paper. Then $20$ balls are selected (without replacement) out of the bag at random.

(b) What is the probability that none of your numbers is selected?
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Total no. of possible  outcomes are $\binom{80}{20}$

Since none of the numbers get matched it means that all the 20 balls must have been selected from the remaining 70 numbers.

So probability that that none of the numbers is selected = $\frac{\binom{70}{20}}{\binom{80}{20}}$
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