- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 10. Principles of Counting

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**CFA Practice Question**

An individual has two different portfolios that he has been investing in. One portfolio was created for his son and has 5 stocks. The other portfolio he created for himself; it has 7 stocks. He has decided that he will keep, sell, or donate the stocks in his portfolio; he will either keep or sell the stocks in his son's portfolio. How many possible outcomes does this individual face for all the stocks in both portfolios?

A. 4,096

B. 69,984

C. 531,441

**Explanation:**The number of possible outcomes is:2

^{5}(3

^{7}) = 69,984.

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**User Contributed Comments**
5

User |
Comment |
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sonderfall |
Keep, sell, donate in his portfolio = 3 poss. / combined with the 7 stocks Keep or sell in his son's portfolio = 2 poss. / combined with the 5 stocks Hope that helps |

whoi |
there's no restriction within this example, therefore the solution must be the max. outcome of all possibilities: - for every share in PF 1 there are 3 possibilities. There are 7 Shares. Thus, possible outcomes are 3^7 - same for PF 2: 2^5 - combine possibility of both portfolio (exclusive ...) : multiplication: 2^5*3^7 |

aakash1108 |
@whoi. thank you! |

Moringa1 |
Please assist how can we solve this using the BA11 Plus Professional ? |

edrei7 |
The permutation (order matters since the stocks are distinct) formula where repetition is allowed is n^r. |