$6)$ For the sequence $8,9,5,7,0,2,3,1,6,4,40$ pt $($Note: you don$$t have to sort this data to get the answers$)$

An $$inversion$$ is any pair that is in the wrong order. They don$$t have to be next to each other.

a$)$ How many inversions are there in the above sequence? $($List them$)$

b$)$ How many inversions are there if you exchange the $9$ and the $1$ in the sequence?

$($This is the new sequence $8,1,5,7,0,2,3,9,6,4)?$

c$)$ What is the maximum number of inversions in a reverse sorted $($worst case$)$ sequence of N numbers? $($This

question is not related to parts a and b$.$ N is a variable and can have any positive value $>=2,$ so give me the

answer in terms of N$).($Suggestion: Try a few sequences to see if your answer makes sense$)$