# Therefore there are only 8 2 20160 seating

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Therefore there are only 8! / 2 = 20160 seating arrangements which are noticeably different. (c) If the relative seating positions around a circular table are the only concern, then we may fix one person and permute the position of the remaining 2

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SERIES A No.3 : ANSWERS five to derive 5! = 240 different arrangements. Alternatively, permute the 6 people and then divide the number of seating arrangements by 6 in recognition of the fact that we do not wish to distinguish amongst arrangements which are derived by rotating. Finally, if we are unconcerned about whether a person sits on the left or the right of another, then we must allow the order of the persons seated around the tabel to be reversed. In that case, we can divide by 2 to derive 120 different arrangements. 6. Ten balls are tossed into four boxes so that each ball is equally likely to fall into any box. What is the probability density function for the number of balls in the last box? Answer: We have a binomial distribution b ( n = 10 , p = 1 4 ) = 10! (10 x )! x ! 1 4 x 3 4 10 x . 7. Ten percent of the words spoken by a politician are “Er”. How many words must he speak so that the probability of at least one “Er”is 0.95? Answer: On the assumption that the spoken word is a Bernoulli trial, the probability of at least one “Er”in n words is 1 P (no “Er”) = 1 (0 . 9) n .
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