I\'m not understanding some part from the solution The question: How many elemen

Question

I'm not understanding some part from the solution

The question:

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 elements, 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?

The answer:

My question: Why 4,6,4 here? From where they are coming? please explain it to me

THanks!!

Let us consider the following four sets A1, A2, A3,A4 Therefore, for 100 An 50 An 25 Ain Comment Step 2 of 2 A We use principle of inclusion-exclusion to find the number of elements in the union of four sets. An Ann Aan 4 (100)-6(50)+4(25)-5

Explanation / Answer

By Inclusion-Exclusion principle:
(100)*C(4, 1) - (50)*C(4, 2) + 25C(4, 3) - (5)*C(4, 4)
=(4*100)-(50*6)+(25*4)-(5*1)

=400-300+100-5

=195

Hence 4 is coming from 4C1

6 is from 4C2

4 is fromm 4C3

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