Question

An analyst issues buy, hold, and sell recommendations on the 12 stocks that he follows. If his opinion on the overall direction of the market is neutral, he expects the stocks to be assigned with two buys, eight holds, and two sells. How many ways can the 12 stocks be assigned the three labels assuming he has a neutral outlook for the market?

Group of answer choices

A. 312,400 ways.

B. 2,970 ways.

C. 1,623,450 ways.

Answer 1

Solution:

Given:

Total number of stocks = n = 12

If analysts opinion on the overall direction of the market is neutral, he expects the stocks to be assigned with two buys, eight holds, and two sells.

Thus analyst can select any 2 stocks to buy out of 12 stocks in ₁₂C₂ ways.

Thus we have 12-2 = 10 remaining stocks

Thus he can select any 8 stocks to hold out of 10 stocks in ₁₀C₈ ways

Thus we have 10-8 = 2 remaining stocks.

Thus he can select any 2 stocks to sell out of 2 stocks in ₂C₂ ways

Thus total number of ways in which 12 stocks be assigned the three labels assuming he has a neutral outlook for the market are:

Total number of ways = ₁₂C₂ X ₁₀C₈ X ₂C₂

We use following combination formula:

Thus

Total number of ways = ₁₂C₂ X ₁₀C₈ X ₂C₂

Total number of ways = 66 X 45 X 1

Total number of ways = 2970 ways

Thus correct answer is: B. 2,970 ways.