Set Theory Question(inclusion-exclusion principle related)

[camcool21]

Homework Statement

An auto insurance has 10,000 policyholders. Each policyholder is classified as:

(i) young or old;
(ii) male or female;
(iii) married or single.
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Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classied as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young married males. How many of the company's policyholders are young, female, and single?
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Homework Equations

$$|A \cup B| = |A| + |B| - |A \cap B|$$​

The Attempt at a Solution

Y = young, O = old
M = male, F = female
MR = married, S = single
n(Y) = 3000
n(O) = 10000 - 3000 = 7000,
n(M) = 4600,
n(F) = 10000 - 4600 = 5400
n(MR) = 7000
n(S) = 10000 - 7000 = 3000
n(Y∩M) = 1320
n(MR∩M) = 3010
n(Y∩MR) = 1400
n(Y∩MR∩M) = 600

Try to find n(Y∩F∩S)?
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That's all I can get from the question. This is starred in my textbook as a difficult problem. Any thoughts?

 

[Slats18]

There is a few more you could write down. For instance, there are 3000 young people, and you know that 1320 of them are young males. Can you make a statement about how many young females there are, and then use this method to find other amounts?

 

[Ray Vickson]

Let ysm,osm,ymm,omm = number of young single males, old single males, young married males and old married males, respectively. Similarly, define ysf, osf, ymf,omf. You are given a total of 8 conditions involving these 8 variables.

RGV