required solution of Q6 so do only Q6 for reference I giving other if you did best I will upvote you I need urgent in an hour so please do quick I will upvote you and don't copy.

2. (5 -ints) Drppuse m,n,w and e are integers with mn>0,mw>0, ne>0 and we. Imagine that a lottery ticket t consists of an unordered subset. of n integers drawn from {1,2,,m}. The state running the lottery picks an unordered subset A of w elements from {1,2,,m}. We will say t is a winning ticket if #(tA)e. Define D(m,n,w,e) to be the minimal size of a set S of tickets with the property that for all possible choices of A, there is a winning ticket in S. Explain why D(46,6,6,3) is the smallest number of tickets in the Winfall lottery that someone can buy and be guaranteed to win a prize. 3. (1n - . Show that D(m,n,w,1)1+nm. Is this ever an equality? 4. A What is D(m,n,w,e) if m=n or m=w ? 5. 1. Show that if m>ne>1 and m>we>1 one has (m,n,w,e)D(m1,n,w,e)+D(m1,n1,w1,e1) (Hints: First choose tickets with numbers from {1,,m1}. Then supplement this choice with tickets that all contain m.) 6. (nn n use Problems 3 and 5 to show that for fixed n and w, there are bounds of the torm D(m,n,w,2)2(n2)m2+am+b D(m,n,w,36(n2)m3+cm2+dm+e where a,b,c,d and e are constants that you don't need to determine and which depend on n and w. You can use without proof the equalities q=1rq=2r(r1)andq=1rq2=6r(r+1)(2t+1) for all integers r1