In a survey conducted by Helena, a financial consultant, it was revealed of her 400 clients
273 own stocks.
185 own bonds.
169 own mutual funds.
106 own both stocks and bonds.
101 own both stocks and mutual funds.
96 own both bonds and mutual funds.
How many of Helena's clients own stocks, bonds, and mutual funds?
(273+185+169) - (106+101+96) + x = 400
x=76 own all three
To find out how many of Helena's clients own stocks, bonds, and mutual funds, we first need to determine the number of clients who own stocks, bonds, or mutual funds individually.
We can do this by adding the number of clients who own stocks, bonds, and mutual funds individually:
273 (clients who own stocks) + 185 (clients who own bonds) + 169 (clients who own mutual funds)
Now, let's calculate this:
273 + 185 + 169 = 627
However, the above calculation counts some clients twice because it includes clients who own both stocks and bonds, both stocks and mutual funds, and both bonds and mutual funds.
To get the correct number of clients who own stocks, bonds, and mutual funds, we subtract the number of clients who own both stocks and bonds, both stocks and mutual funds, and both bonds and mutual funds from the total calculated above.
Let's continue the calculation:
627 - 106 (clients who own both stocks and bonds) - 101 (clients who own both stocks and mutual funds) - 96 (clients who own both bonds and mutual funds)
Now, let's calculate this:
627 - 106 - 101 - 96 = 324
Therefore, 324 of Helena's clients own stocks, bonds, and mutual funds.
To find out how many of Helena's clients own stocks, bonds, and mutual funds, you'll need to use the principle of inclusion-exclusion.
1. Start by adding up the number of clients who own stocks, bonds, and mutual funds individually:
- Stocks (273)
- Bonds (185)
- Mutual Funds (169)
2. Now, subtract the number of clients who own both stocks and bonds, both stocks and mutual funds, as well as both bonds and mutual funds. These clients were double-counted in the individual counts:
- Both stocks and bonds (106)
- Both stocks and mutual funds (101)
- Both bonds and mutual funds (96)
3. To get the count of clients who own all three (stocks, bonds, and mutual funds), subtract the double-counted clients from the sum of individual counts:
- Total = Stocks + Bonds + Mutual Funds - (Both stocks and bonds + Both stocks and mutual funds + Both bonds and mutual funds)
- Total = 273 + 185 + 169 - (106 + 101 + 96)
- Total = 627 - 303
- Total = 324
Therefore, 324 of Helena's clients own stocks, bonds, and mutual funds.