There are four large groups of people, each with 1000 members. any two of these groups have 100 members in common. any three of these groups have 10 members in common. and there is 1 person in all four groups. all together, how many people are in these groups?

3,359

Step-by-step explanation:

Let A, B, C and D the four groups of people.

Let us denote with |A| the number of elements in a set A.

Then the number of elements of A∪B∪C∪D is the sum of the elements in each group subtracting the elements that have been counted twice.

That is,

|A∪B∪C∪D |=|A|+|B|+|C|+|D| - |A∩B| - |A∩C| - |A∩D| - |B∩C| -  |B∩D|- |C∩D| - |A∩B∩C| - |A∩B∩D| - |A∩C∩D| - |B∩C∩ D| - |A∩ B∩C∩ D| =

1000+1000+1000+1000 - 100 - 100 - 100 - 100 - 100 - 100 - 10- 10- 10- 10 - 1 = 3359

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.