Your broker has suggested that you diversify your investment

Your broker has suggested that you diversify your investments by splitting your portfolio among mutual funds, municipal bond funds, stocks, and precious metals. She suggests six good mutual funds, six municipal bond funds, five stocks, and three precious metals (gold, silver, and platinum).

(a) Assuming your portfolio is to contain one of each type of investment, how many different portfolios are possible?
_____ choices

(b) Assuming your portfolio is to contain five mutual funds, five municipal bond funds, one stock, and two precious metals, how many different portfolios are possible?
______ choices

Solution

Ans:a) Out of all the different investment options we have to choose one from each. We know that we can choose \'r\' quantities from total \'n\' options using formula nCr which is equal to (n!)/((n-r)! *(r!)) where n! Denotes factorial of n.

(6C1)*(6C1)*(5C1)*(3C1) = 6*6*5*3 = 540 different options to choose from.

b) Now we have to choose 5 mutual funds out of 6, 5 municipal bonds out of 6, 1 stock out of 5, 2 metals out of 3.

So total no. of choices are (6C5)*(6C5)*(5C1)*(3C2) = 6*6*5*3 = 540 Different options.