Question: (a) In how many ways can the integers 1, 2, 3, . . . , n be arranged in a line so that none of

(a) In how many ways can the integers 1, 2, 3, . . . , n be arranged in a line so that none of the patterns 12, 23, 34,..., (n - 1)n occurs?
(b) Show that the result in part (a) equals dn-1 + dn. (dn = the number of derangements of 1, 2, 3, ..., n.)

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