请教两道数学JJ 急！

benniexu

 三男三女看电影，票是同排联号的，男女间隔坐，几种坐法

JJ作者给的答案是P33*P33*2，我怎么觉得应该是C43*P33*P33呀？？

Juniors can study physics and calculus, but juniors who study physics can not study Economics. Juniors can study both calculus and Economics. 15 juniors study physics, 35 study calculus, 22 study Ecomomics, and 17 study both calculus and Econimics. Question: how many juniors study at least one of these three courses?

选P的有15，如果选P的都选C，那么总人数最少，15＋（35－17－15）＋22

蓝色字体是作者的答案，我不明白为什么35-17后还要再减一个15呀？？

麻烦XDJM们给我讲讲~~~谢谢啦~~~~~

sycrwang

三男三女看电影，票是同排联号的，男女间隔坐，几种坐法

2 steps: (1)先排3男, 如占据1,3,5, 则有P33, (2)在排女,占据2,4,6, 有P33

          故 总数为: P33*P33;

 在颠倒男女次序, 故需*2-->  2P33*P33

Juniors can study physics and calculus, but juniors who study physics can not study Economics. Juniors can study both calculus and Economics. 15 juniors study physics, 35 study calculus, 22 study Ecomomics, and 17 study both calculus and Econimics. Question: how many juniors study at least one of these three courses?

   因为选物理的15人,有可能都选CAL, 故他们最大可duplication is 15, the least possiblity is 0.  the question is to ask you the least number: 

so, you should consider all juniors who have choosen physics   
 have selected calculs as well.

the number=  physics (15)+economy(22) - duplication(cal =35 - 15- 17) =40

如问最大可能: 15+ 22+(35-0-17) = 55

[此贴子已经被作者于2008-6-29 2:13:19编辑过]

benniexu

太感谢了！！！真是大好人呀！！！