2. 外语
  3. A university gives each student a student number, which consists of either three digits (between 0 and 9, inclusive) followed by

A university gives each student a student number, which consists of either three digits (between 0 and 9, inclusive) followed by

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问题 A university gives each student a student number, which consists of either three digits (between 0 and 9, inclusive) followed by two letters or three letters followed by two digits. For example, 055-XY, 123-PP, and AAA-70 are all acceptable student number. How many different numbers can the university issue?
选项
答案2,433,600种
解析 学号一共有两类情况：
(1)3个数字+2个字母；
(2)3个字母+2个数字。
第(1)类情况下，要先挑选3个数字，再挑选2个字母，则分为5个步骤；每个数字有10种选择，每个字母有26种选择，则第一种情况共有10×10×10×26×26=676,000种选择；第(2)类情况下，同理有26×26×26×10×10=1,757,600种选择。两类情况下可能的结果应采用加法原理，则共有676,000+1,757,600=2,433,600种学生编号可以发放。
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