Suppose we have 20 balls numbered 1,2,...,20. Each day we pick a single ball randomly.1) What's the probability of picking all 20 balls in 22 days ?2) What's the probability of picking only 1and2 in 4 days (Atleast 1 times each) ?

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Suppose we have 20 balls numbered 1,2,...,20. Each day we pick a single ball randomly.1) What&#039;s the probability of picking all 20 balls in 22 days ?2) What&#039;s the probability of picking only 1and2 in 4 days (Atleast 1 times each) ?

Layla Love · Accepted Answer

For the (1), your approach is not quite correct. The problem is that the procedure you outlined will over-count some of the ways to choose the balls. For example consider the following two ways of following your instructions:Option 1:1) Pick the days numbered 1,2,…,19,20.2) On these days, pick balls numbered 1,2,…,19,20.3) On days 21 and 22, pick ball 20.Option 2:1) Pick the days numbered 1,2,…,19,21.2) On these days, pick balls numbered 1,2,…,19,20.3) On days 20 and 22, pick ball 20.These both result in the same ball distribution, but are counted separately by your method. The other solution you wrote uses careful accounting to avoid this.For (2), you are answering a different question than the other solution. You are counting the number of ways to pick four balls comprising one 1s and 2s, with both present. The other method is the number of ways to pick four balls where at least one is a 1 and at least one is a 2.

Suppose we have 20 balls numbered 1,2,...,20. Each day we

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