CFA Level IQuantitative MethodsEasy
A portfolio manager wants to select 3 stocks from a list of 8 candidates to build a small equity portfolio. The order in which the stocks are chosen does not matter. How many different 3-stock portfolios can be formed?
- A24
- B336
- C512
- D56
Show answer & explanationAnswer & explanation
Correct answer: D. 56
Since order doesn't matter, use combinations: nCr = 8!/(3!(8-3)!) = 8!/(3!5!) = (8×7×6)/(3×2×1) = 336/6 = 56.
Why the other options are wrong
- A. Incorrect; does not correspond to any standard combinatorial formula for this problem.
- B. This is the permutation count (8P3), which incorrectly treats order as relevant.
- C. This equals 8^3, treating selections as independent with repetition, which is wrong here.
Combination Formula (nCr)
Counts the number of ways to choose r items from n items when order does not matter, calculated as n!/(r!(n-r)!).
- Use combinations when order is irrelevant (e.g., selecting a portfolio)
- Use permutations when order matters (e.g., ranking top 3 stocks)
- Combinations are always ≤ permutations for the same n and r
Memory trick: Combo doesn't care about the order, Permutation puts it in order