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?
Click on the arrows to vote for the correct answer
A. B. C. D.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)!. Here, it is 8! / (8-4)! = 8 * 7 * 6 * 5 = 1,680.