Final answer:
By using the principle of inclusion and exclusion, it is determined that 110 people in a population of 450 cannot speak English, Hindi, or Tamil.
Step-by-step explanation:
To find out the number of people who can speak neither English, Hindi, nor Tamil in a population of 450 people, we will use the principle of inclusion and exclusion. We know the following:
- 205 can speak English
- 210 can speak Hindi
- 120 can speak Tamil
- 100 can speak both English and Hindi
- 35 can speak both English and Tamil
- 80 can speak both Hindi and Tamil
- 20 can speak all three languages
First, we add the numbers of people who can speak each language:
205 (English) + 210 (Hindi) + 120 (Tamil) = 535
This total counts people who can speak two or three of the languages more than once. To correct this, we subtract the numbers of people who can speak two languages:
535 - (100 + 35 + 80) = 320
We have subtracted those who can speak two languages twice, but now we have subtracted those who can speak all three languages twice, so we must add them back once:
320 + 20 = 340
This gives us the number of people who can speak at least one of the languages. To find out how many people can't speak any, we subtract this number from the total population:
450 (total population) - 340 (can speak at least one language) = 110
Therefore, 110 people cannot speak English, Hindi, or Tamil.