Question

In a survey conducted by Helena, a financial consultant, it was revealed of her 426 clients

288 own stocks.
200 own bonds.
184 own mutual funds.
123 own both stocks and bonds.
106 own both stocks and mutual funds.
102 own both bonds and mutual funds.

How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.)
_______clients

Answer 1

Answer: There are 85 Helena's client own stocks, bonds and mutual funds.

Explanation:

Since we have given that

Let A: who own stocks

B : who own bonds

C : who own mutual fund

So, According to question,

n(A) = 288

n(B) = 200

n(C) = 184

n(A∩B) = 123

n(B∩C) = 106

n( A∩C) = 102

n(A∪B∪C) = 426

As we know the formula :

`n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\426=288+200+184-123-106-102+n(A\cap B\cap C)\\\\426-341=n(A\cap B\cap C)\\\\85=n(A\cap B\cap C)`

Hence, there are 85 Helena's client own stocks, bonds and mutual funds.