I have 4 questions and i would be indebted to anyone can help me


1. Find the value of each of the following quantities:
a) C(5,1)
b) C(8,8)
c) C(8,0)
C means Combination

2. How many bit strings of length 10 have:
a) exactly three 0s?
b) the same number of 0s as 1a?
c) at least seven 1s?
d) at least three 1s?

3. Find the cofficient of x^5 y^8 in (x+y)^13.

4. Show that if n is a positive integer, then C(2n,2)=2C(n,2)+n^2
a) by using a combinatorial argument.
b) by algebraic mainpulation.


thanks in advace.