求解：2條Applied math 概率

Question 1 :

A novel consisting of n ( >4) similar volumes is kept on a shelf with the volumes
in correct numerical order, that is , with volume 1 on the left, volume 2 next , and so on, the volumes are all taken down for cleaning and are replaced on the shelf in random order. Find the probability of finding exactly (i). n ,(ii). n-1 ,**(iii) n-2
**(iv) n-3 volumes in their correct positions on the shelf.

Question 2 :

the digit 1, 2 , ..., 7 are arranged randomly to form a 7-digit number. Find the
probability that
(a) the number is divisible by 2
(b) the number is divisible by 4
**(c) digits 1, 2 , 3 appear consecutively in the proper order
**(d) digits 1 , 2, 3 appear in the proper order but not consecutively

Ｒｅｍａｒｋ：
(**)題 希望解答者可以略作解釋