Question

If 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. Determine how many speak
either French or Russian or Spanish?

Answer 1

Given: 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.

To find: Faculty members who either speak French or Russian or Spanish

Explanation: 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

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

Therefore, number of faculty members who speak either Spanish or French or Russian is 245.