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jingyunmao

From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight.
how many diffrerent crews of this type are possible?
答案是432， 谁能告诉我怎么做的么- -

JoshwuS

C（2,9）*12    9个人里面取两个，然后剩下一个12个里面选一个，相乘得432

jingyunmao

还是没动- - 能具体解释下么...

pennmou

12 people with previous experience in space flight， you have to choose exactly 1 person, so you have 12 ways to do that. And from the rest 9 people, you have to choose 2 of them, so it is 9*8=72, but wait, remember in this question order doesn't matter, so AB is the same as BA,(in 9*8, we assume that order matters, you choose A first and then B is one order and if choose B first and then A it is another order)  then you have to divide 72 by 2, that will get you 36.

so the total ways=36*12

jingyunmao

悲剧了... 我题目问的看错了... 我以为他问的是...一共有多少种crew的可能性... 大前提是每个crew都有一个experienced...
谢谢啦...