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    manayay Posts: 2, Reputation: 1
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    Sep 23, 2013, 09:38 PM
    I have 5 identical balls and I have three buckets which are labelled A, B, C. (a) In
    I have 5 identical balls and I have three buckets which are
    labelled A, B, C.
    (a) In how many different ways can I put the five balls into the buckets.
    (There are no constraints, e.g. a bucket can be empty.)
    (b) In how many different ways can I put the five balls into the buckets if
    each bucket must contain at least one ball?
    Now suppose I perform the following experiment. For each ball I pick one of
    the three buckets with equal probability and put the ball in that bucket. I
    claim that the probability that each bucket has at least one ball is 50/81. One
    might think this probability would be given by your answer to (b) divided
    by your answer to (a), which should work out to 2/7.
    (c) Explain why your answer to (b) divided by your answer to (a) is not the
    correct probability.
    (d) Derive my answer.

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