Question

A trader is designing his investment portfolio. He has prepared a list of potential companies in which to purchase stock. These include 3 companies in agriculture, 4 companies in manufacturing and 6 companies in the high-tech industry. The trader is going to print this list of companies. a. In how many ways can he print the list? b. What is the probability that the last 2 companies in the list are manufacturing? c. What is the probability that none of the agricultural companies are together in the list? d. If we just look at the categories of the companies, how many ways are there in which to print the list? e. The trader will select 5 stocks from the list in which he will invest. How many ways can he select these? f.Of the 5 selected stocks what is the probability that he will pick at least 2 high-tech stocks? g. Of the 5 selected stocks what is the probability that the trader's pick contains 2 in agriculture, 1 in manufacturing and 2 in high-tech industry?

Answer 1

Explanation:

(a) The required number of ways = 13! = 6,227,020,800

(b) The required probability = 4C2/13C2 = 1/13

(c) The required probability = 1 - P(at least two of the agricultural companies are together in the list)

= 1 - 3C2*2!*12!/13! = 7/13

(d) The required number of ways to print the list = 13!/(3!*4!*6!)

= 60,060

(e) The required number of ways = 13C5 = 1287

(f) The required probability

= (6C2*7C3 + 6C3*7C2 + 6C4*7C1 + 6C5)/13C5

= 0.8205

(g) The required probability = (3C2*4C1*6C2)/13C5 = 0.1399