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Florence · 2022年01月04日

这道题包含两个问题？

  1. CFA I
  2. Quantitative

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：

A.

142,506

B.

17,100,720

C.

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：

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

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 = 17,100,720

​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？

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1 个答案

星星_品职助教 · 2022年01月04日

同学你好，

只有一个问题。

第二段问的是“What are the chances of winning if ……”，这相当于在问一个概率（chance），即30只股票中随机选出5只，这个选择正好是最终correct order的概率是多少。

根据排列方法计算出的17,100,720只是这个概率的分母。

所以，第二段后面的“ ……a contestant’s chance of winning is one out of：” 相当于在问这个分母是多少，最终的“chance”其实是1 / 17,100,720 （one out of 17,100,720）

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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)!}}n​Pr​=(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 = 17,100,72030​P5​=(30−5)!30!​=25!30!​=30×29×28×27×26=17,100,720 老师，第一大段看不明白，可以翻译吗？

2022-11-18 16:51 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.142,506B.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)!}}n​Pr​=(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 = 17,100,72030​P5​=(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!}}n​Pr​=(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 = 17,100,72030​P5​=(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!}}n​Pr​=(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 = 17,100,72030​P5​=(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