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NO.PZ2021062201000008

问题如下：

Gerd Sturm wants to sponsor a contest with a $1 million prize. The winner must pick the stocks that will be the top five performers next year among the 30 stocks in a well-known large-cap stock index. He asks you to estimate the chances that contestants can win the contest.

What are the chances of winning if the contestants must pick the five stocks in the correct order of their total return? If choosing five stocks randomly, a contestant’s chance of winning is one out of:

选项：

142,506

17,100,720

24,300,000

解释：

B is correct. The number of permutations is the number of ways to pick five tocks out of 30 in the correct order：

${}_n{P_r} = \frac{{n!}}{{(n - r)!}}$

${}_{30}{P_5} = \frac{{30!}}{{(30 - 5)!}} = \frac{{30!}}{{25!}} = 30 \times 29 \times 28 \times 27 \times 26 = 17,100,720$

老师，第一大段看不明白，可以翻译吗？

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星星_品职助教 · 2022年11月18日

同学你好，

第一段的有效信息为：如果想赢得奖金，则winner必须从30只股票中挑出5只表现最好的。

第二段在这个基础上又增加了要排序的条件。即如果想中奖，那么只挑出来表现前五名的股票是不够的，还需要根据正确的顺序选中第一名到第五名（in the correct order）。这个条件说明本题是一个排列问题，不是组合问题。

综上，由于从30只股票中有顺序的挑出表现最好的五只股票一共有 30P5=17,100,720种可能，所以一个人随机挑五只股票，就正好选中了最终表现最好的第一名到第五名的概率就是1/17,100,720。

因为题目只问分母是多少（chance of winning is one out of...），所以直接选择B选项即可。

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NO.PZ2021062201000008问题如下 GerSturm wants to sponsor a contest with a $1 million prize. The winner must pithe stocks thwill the top five performers next yeamong the 30 stocks in a well-known large-cstoinx. He asks you to estimate the chances thcontestants cwin the contest. Whare the chances of winning if the contestants must pithe five stocks in the correorr of their totreturn? If choosing five stocks ranmly, a contestant’s chanof winning is one out of: A.142,506B.17,100,720C.24,300,000 B is correct. The number of permutations is the number of ways to pifive tocks out of 30 in the correorrnPr=n!(n−r)!{}_n{P_r} = \frac{{n!}}{{(n - r)!}}nPr=(n−r)!n!30P5=30!(30−5)!=30!25!=30×29×28×27×26=17,100,720{}_{30}{P_5} = \frac{{30!}}{{(30 - 5)!}} = \frac{{30!}}{{25!}} = 30 \times 29 \times 28 \times 27 \times 26 = 17,100,72030P5=(30−5)!30!=25!30!=30×29×28×27×26=17,100,720 老师好，请问为什么要剪5之后排列？

2022-08-14 13:58 1 · 回答

NO.PZ2021062201000008问题如下 GerSturm wants to sponsor a contest with a $1 million prize. The winner must pithe stocks thwill the top five performers next yeamong the 30 stocks in a well-known large-cstoinx. He asks you to estimate the chances thcontestants cwin the contest. Whare the chances of winning if the contestants must pithe five stocks in the correorr of their totreturn? If choosing five stocks ranmly, a contestant’s chanof winning is one out of: A.142,506 B.17,100,720 C.24,300,000 B is correct. The number of permutations is the number of ways to pifive tocks out of 30 in the correorrnPr=n!(n−r)!r!{}_n{P_r} = \frac{{n!}}{{(n - r)!r!}}nPr=(n−r)!r!n!30P5=30!(30−5)!=30!25!=30×29×28×27×26=17,100,720{}_{30}{P_5} = \frac{{30!}}{{(30 - 5)!}} = \frac{{30!}}{{25!}} = 30 \times 29 \times 28 \times 27 \times 26 = 17,100,72030P5=(30−5)!30!=25!30!=30×29×28×27×26=17,100,720 題目先說， must pithe five stocks in the correorr 。之後又說， choosing five stocks ranmly, 所以請問究竟是 in correorr 還是ranmly, 是需要排序，還是不需要排序？謝謝

2022-04-15 14:09 1 · 回答

NO.PZ2021062201000008 17,100,720 24,300,000 B is correct. The number of permutations is the number of ways to pifive tocks out of 30 in the correorr nPr=n!(n−r)!r!{}_n{P_r} = \frac{{n!}}{{(n - r)!r!}}nPr=(n−r)!r!n! 30P5=30!(30−5)!=30!25!=30×29×28×27×26=17,100,720{}_{30}{P_5} = \frac{{30!}}{{(30 - 5)!}} = \frac{{30!}}{{25!}} = 30 \times 29 \times 28 \times 27 \times 26 = 17,100,72030P5=(30−5)!30!=25!30!=30×29×28×27×26=17,100,720 从题里面，哪里可以看出是需要排序的呢？

2022-01-17 15:55 1 · 回答

NO.PZ2021062201000008 17,100,720 24,300,000 B is correct. The number of permutations is the number of ways to pifive tocks out of 30 in the correorr nPr=n!(n−r)!r!{}_n{P_r} = \frac{{n!}}{{(n - r)!r!}}nPr=(n−r)!r!n! 30P5=30!(30−5)!=30!25!=30×29×28×27×26=17,100,720{}_{30}{P_5} = \frac{{30!}}{{(30 - 5)!}} = \frac{{30!}}{{25!}} = 30 \times 29 \times 28 \times 27 \times 26 = 17,100,72030P5=(30−5)!30!=25!30!=30×29×28×27×26=17,100,720 您好，按照我的理解，这道题的题干第二段包含两个问题，第一个问题是排列问题，选择B，第二个问题是组合问题，随机从30支股票中选出5个，答案选择A？

2022-01-04 14:32 1 · 回答

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