Question

Suppose that 200 faculty members can speak French and 50 can
speak Russian, while only 20 can speak both French and Russian.
Apply the principle of inclusion-exclusion to find the number of
faculty members who can speak either French or Russian.​

Answer 1

Answer:

Number of faculty members who speak either Spanish or French or Russian is 245.

Explanation:

Step 1: There are 200 faculty members that speak French, 50 that speak Russian, 100 that speak Spanish, 20 that speak French and Russian, 60 that speak French and Spanish, 35 that speak Russian and Spanish, while only 10 that speak French, Russian and Spanish.

Step 2: Faculty members who either speak French or Russian or Spanish

Step 3: Let the number of people speaking French be n(A), number of people speaking Russian be n(B) and number of people speaking Spanish be n(C)

n(A) = 200

n(B) = 50

n(C) = 100

Step 4: People who speak French and Russian can be denoted by n(A∩B)= 20

People who speak French and Spanish can be denoted by n(A∩C)= 60

People who speak Spanish and Russian can be denoted by n(C∩B)= 35

People who speak French, Russian and Spanish can be denoted by n(A∩B∩C)= 10

We need to find people who speake either of the language. It is denoted by n(A∪B∪C).

The formula for finding this is given by:

n(A∪B∪C)

= n(A)+n(B)+n(C) -n(A∩B -n(A∩C) -n(C∩B)+n(A∩B∩C)

=200+50+100-20-60-35+10

= 245

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