Moreover these probabilities are independent

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the next arrival. Moreover, these probabilities are independent. Therefore the probability that another five buses will pass before the 106 arrives is just P (277 254) 5 P (106) = 1 4 3 4 5 ; and this holds regardless of the fact that three buses which were not the 106 have already passed. 4. Six dice are tossed. What is the probability that every possible number will occur? Answer: The number of possible outcomes from throwing the six dice is 6 6 . The number of outcomes which are favourable to the event in question is the number of permutations of the integers 1 , 2 , . . . , 6 which is 6!. Therefore Probability of the event = Number of outcomes favourable to the event Total number of outcomes = 6! 6 6 = 5 × 4 6 4 = 0 . 015432 . 5. How many ways can six people sit down to a table laid for six? How many ways if the table is laid for eight? How many ways if the only concern is who sits next to whom? Answer: (a) Six people at a table laid for 6 can sit in 6! = 720 different ways. (b) If the table were laid for eight and there were eight people, then the num- ber of ways would be 8! Imagine that there are six living persons and two ghosts: the ghost of Hamlets father and the ghost of Banquo. They can interchange their seating positions without the other persons noticing.

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