# Principle of Inclusion of Exclusion

• Dec 10th 2008, 10:25 AM
flwer_13
Principle of Inclusion of Exclusion
Bently Chalk Brush Manufacturing Company has 900 employees: 615 are female, 345 are union members, and 482 are single. 295 are single females, 187 are single union members, 190 are female union members, and 120 are single female union members. How many workers are female or union members or single?

* use venn diagram and principle
• Dec 10th 2008, 11:41 AM
Venn diagram
Hi-

Quote:

Originally Posted by flwer_13
Bently Chalk Brush Manufacturing Company has 900 employees: 615 are female, 345 are union members, and 482 are single. 295 are single females, 187 are single union members, 190 are female union members, and 120 are single female union members. How many workers are female or union members or single?

* use venn diagram and principle

I attach a Venn diagram in which I've started to put the numbers. You'll see that I've started in the middle: the single female union members, 120 of them. There are 190 female union members altogether, so there must be 70 who aren't single. Where do they go on the diagram?

Continue to work outwards, subtracting as you go, until you've worked out how many go in each region.

• Dec 10th 2008, 12:15 PM
Soroban
Hello, flwer_13!

Quote:

Bently Chalk Brush Manufacturing Company has 900 employees:

482 are Single,
615 are Female,
345 are Union members,

295 are Single Females,
190 are Female Union members,
187 are Single Union members,

and 120 are Single Female Union members.

How many workers are Single or Female or Union members?

* Use Venn diagram and principle.

There is a formula for this situation . . .

\$\displaystyle n(S \cup F \cup U) \;=\;\underbrace{n(S)}_{482} + \underbrace{n(F)}_{615} + \underbrace{n(U)}_{345}\$

. . . . . . . . . . . . \$\displaystyle - \underbrace{n(S\cap F)}_{295} - \underbrace{n(F \cap U)}_{190} - \underbrace{n(S \cap U)}_{187}\$

. . . . . . . . . . . . . . . \$\displaystyle + \underbrace{n(S \cap F \cap U)}_{120}\$

Therefore: .\$\displaystyle n(S \cup F \cup U) \;=\;\boxed{890}\$