Advanced Combinatorics

Hope you can help me to find the answer(萬分感激)
1.Expand(-1+2x)^n

2.Find A,B,C and D such that k^4=A(kC4)+B(kC3)+C(kC2)+D(kC1)for any positove integer k≧4 and hence find 1^4+2^4+......+n^4

3.(a)Prove that 〖n2〗^(n-1)=∑_(k=1)^n▒(n¦k)
(b)We can prove the above result by the following combinatorial argument:
(i)In a group of n people,k of them wil form a team and among them onr eill be elected as the team leader.In how many ways can this team of k members br formed?
(ii)In a group of n people,a team leader is chosen.Then the team leader can choose his team member(s) to form a team(of any size).In how many ways can this team be formed?
(iii)By using(i)and(ii),re-prove(a).

4.By considering (1+x)^n+1,show that(2^(n+1)-1)/(n+1)=1+1/2 nC1+1/3 nC2+⋯ 1/(n+1) nCn

5.Show that(nC0)(nC1)+(nC1)(nC2)+...+(nCn-1)(nCn)= (2n)!/(n-1)!(n+1)!

唔識做ge可以唔做,請大家識做幾多就做幾多