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- We need to use , t = 10, n = 3 and c = 1/10. Therefore:
- The total number of combinations is: We start by painting 9 of the 20 objects red. There are possible combinations of doing that. Of the remaining 11 objects, we paint 8 white. That can be done in possible combinations. The final three objects are painted blue. Obviously there is only one possible combination of doing that. The total number of possible combinations is therefore: . One might think that the answer would have been different if we would have started by painting the 3 blue objects. The following formula describes the possible combinations by first painting 3 objects blue, followed by 8 objects white: . Indeed, if we would have started by painting the 8 white objects, followed by nine objects red, the formula would have been . So, it doesn’t make any difference where you start. We have shown that:
- This is very similar to the example given in the main text. The probability is:
- This probability can be calculated by adding the probability of 1 king plus the probability on two kings plus the probability on three kings plus the probability of four kings: . It would have been simpler to calculate the probability that no king is drawn and subtracting this from 1: