Quantitative Methods MCQ - Quantitative Methods Section 2

61 The number of ways we can choose r objects from a total of n objects, when the order in which the r objects are listed does matter is given by the permutation formula: Pr = n!/(n – r)! How many permutations are possible when choosing 3 objects from a total of 9 objects?

In this problem, 9! / ( 9 - 3)! = 9! / 6! = 504

62 An investor is considering investing in 8 bonds. According to a new investment policy of a company, an investor can invest in 3 bonds graded AAA, 3 bonds graded AA and 2 graded A. The investor can choose this combination from a pool of 30 bonds available in market. Of the 30 bonds 10 are AAA, 10 are AA and 10 are A. How many different ways are possible for an investor to invest considering the new policy?

The number of ways in which an investor can invest in 3 AAA, 3 AA and 2 A bonds is: 10C3 x 10C3 x 10C2 = 120 x 120 x 45 = 648,000.

63 The number of ways in which three stocks can be sold from a total of 12 stocks, when the order in which the stocks are sold matters, is most likely:

Since the order in which the stocks are sold matters, use the permutation formula: Number of ways = n! / ( n - r )! = 12! / (12 - 3)! = 1320. You may also use the nPr function on the calculator. Note that r is the number of stocks to be selected and n is the total number of stocks.

64 Which of the following methods will you most likely use to count the number of ways for a certain event when the order matters?

Permutation is the method used when the order does matter. The order does not matter in combination and labeling.

65 The number of ways to select 3 stocks from a universe of 10 stocks, given that the order does not matter, is most likely:

Use the combination formula since the order of selection does not matter. Number of ways = n! / [ r! (n - r)! ] = 10! / [3! (10 - 3)! ] = 120. You may also use the nCr function on the calculator. Note that r is the number of stocks to be selected and n is the total number of stocks.