How many elements are in the union of five sets if the sets contain 10,000 elements each, each pair of sets has 1000 common elem

Question

3 years ago

9

ents, each triple of sets has 100 common elements, every four of the sets have 10 common elements, and there is 1 element in all five sets?

1 answer:

masya89 [10] · Answer 1 · 2022-03-02T02:56:08+03:00

Answer:

40951

Step-by-step explanation:

Using the principles of inclusion - Exclusion

Where C(n,r)=n!/(n-r)!r!

Total elements in the five sets including number repetition is given as (10000)×C(5, 1) =10000× 5!/(5-1)!1!=10000×5=50000

Total Number of elements in each pair including number repetition of sets is given as

=(1000) × C(5, 2) =10000

Number of elements in each triple of sets is given as

=(100) × C(5, 3) =1000

Number of elements in every four sets

=(10) × C(5, 4)=50

Number of elements in every one set

(1) × C(5, 5)=1

Therefore total number of unique elements=50000-10000+1000-50+1

=40951