某段铁路上有12个车站,共需要准备普通客票()
- A.24种
- B.66种
- C.132种
- D.144种
正确答案及解析
正确答案
解析
分析:因为车票与两站的顺序有关,从甲站到乙站的车票不同于从乙站到甲站的车票,所以这个问题可以归结为排列问题来解.因为每一张车票对应着2个车站的一个排列,所以需要准备的车票种数,就是从12个车站中任取2个的排列数,即P122=12×11=132(种).
答:C.
注意这是一道排列的直接应用题.在解这类题目时,首先要看能不能把问题归结为排列问题,也就是判断问题是否与排列顺序有关.如果与排列顺序有关,就可能归结为排列问题来解.其次分析在问题里,n个不同元素指的是什么,m个元素指的是什么,从n个元素中每次取出m个元素的每一个排列对应着问题里的什么事件.例如本题中从12个车站每次取出2个车站的一个排列就对应着一种车票.
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