Answer:
3361 people should poll so it's inevitable that at least three people in the sample have identical demographic information.
Step-by-step explanation:
Consider the provided information.
There are 8 age and 7 income groups, 5 gender choices, and 6 choices for ethnicity.
For age we have 8 choices.
For Income groups we have 7 choices.
For gender groups we have 5 choices.
For ethnicity we have 5 choices.
Therefore, the total number of groups is: 8×7×5×6=1680
That means 1680 distinct group.
According to Pigeons holes principal: If m pigeons are in n holes and m > n, then at least 2 pigeons are in the same hole.
So to select at least 2 people in the sample have identical demographic information 1681 people needs to poll.
In order to at least 3 people (2 × 1680+1) people should need to poll.
2 × 1680 + 1 = 3361
Hence, 3361 people should poll so it's inevitable that at least three people in the sample have identical demographic information.
