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**CFA Practice Question**

A portfolio manager has identified three asset classes with 10, 8, and 6 securities respectively. He wants to create a portfolio with only two securities from each asset class. In how many ways can he create his portfolio?

A. 18,900

B. 480

C. 88

**Explanation:**Since only two securities can be selected from each asset class, there are nC2 ways of creating a portfolio. As there are three asset classes, we have

_{10}C

_{2}x

_{8}C

_{2}x

_{6}C

_{2}= 45 x 28 x 15 = 18,900 ways of creating a portfolio.

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**User Contributed Comments**
18

User |
Comment |
---|---|

ljscott |
How do u do this using HP12C?? |

kirstydebs |
Please could someone explain this more clearly? |

dealsoutlook |
damn i added them..gotta stop these silly mistakes :( And they had that answer in there too. Kirstydebs its pretty simple you are required to choose 2 securities from each class and there is no particular order required so you cant use permutations. So you would use nCr. You would "choose" 2 securities from 10, 2 from 8 and 2 from 6. Therefore answer would be 10C2*8C2*6C2 Hope this helps |

SalmaM |
i added them too! |

Analizer |
I know Dealsoutlook has explained it, but I still can't understand how the arithmetic results in 18,900. Can someone explain in a simple fashion how the answer is derived? |

vadklim |
To Analizer: 10C2 (2 securities from 10 possible) = 45 diffirent variants 8C2 = 28 diffirent variants 6C2 = 15 And then use multiplication rule |

haosheng |
No need to use calculator at all, answer A is the only one is huge enough to satisfy the common sense |

MrBruny |
Guys, check the answer for reading 8, question 17 out of the CFA textbooks. Should explain it. |

JHeld |
10C2 = 10!/((10-2)!*2!) Do this for each and apply the muli-Rule. |

uma85 |
On TIBA ... 10C2: type 10 on calc,2nd nCr, type 2, type =. Ans= 45. 8C2: type 8 on calc,2nd nCr, type 2, type =. Ans = 28 6C2: type 6 on calc, 2nd nCr, type 2, type =. Ans= 15 multiply all the ans. 45*28*15= 18,900. |

pepper |
in HP: 10 <g><n!> 2 <g><n!> 10<g><LST x> - <g><n!> X / "-" = minus "X" = multiply "/" = divide |

boddunah |
i added them too. |

altynai |
thanks uma85 |

zeen1 |
damn fell for it and added them too... |

chandsingh |
Im from a poor maths background so i have been having alot of difficulty figuring out what the symbols and answers above mean. So for those who need a more pedantic calculation here it is: 10c2 = 10!/((10-2)*2) = 1*2*3*4*5*6*7*8*9*10 / ((1*2*3*4*5*6*7*8) *2) = 3628800 / 80640 = 45 etc |

Oksanata |
i added them too! |

CalebMast |
Quite nice that the calculator does all of the work. This could be another that involves way too many computations. uma85 - very helpful explanation. |

ajshittu |
Thank you pepper |