- 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**

You are reviewing a list of 8 recommended securities and wish to invest in 4. You will put 40% of your capital in one, 30% in another, 20% in the third, and 10% in the last one. How many different ways can you choose among the 8 securities and invest according to your design?

A. 1,980

B. 1,774

C. 1,680

**Explanation:**The combination, or binomial formula, gives the number of ways that k objects can be chosen from n items, without regard to the order of choosing. The formula is (n choose k) = n! / [k! *(n-k)!]. However, in this case, the order does matter. If we choose stocks 3, 1, 7, and 5, we don't consider that the same as choosing 5, 7, 1 and 3, because the portfolio weights would differ. We need the general permutation formula, which gives the number of ways that k objects can be chosen from n items, with regard to order. The formula is n_P_k = n! / (n-k)!. Therefore 8! / (8-4)! = 8 * 7 * 6 * 5 = 1,680.

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**User Contributed Comments**
2

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

Lamkerst |
imagine 4 boxes for 4 stocks: 1st box may contain 8 stocks 2nd box may contain (8-1) stocks = 7 3rd box may contain (7-1) stocks = 6 4th box may contain (6-1) stocks = 5 overall = 8*7*6*5 = 1680 |

azramirza |
Just use permutation since they r following an order= 8P4=1680 |