I'm doing some warm-up for the starting of the next year.I came across this problem but unfortunately I don't know how to do it but I"m curious how.Any help will be appreciated.Thank you.

Let Z* denote the nonnegative integers,and S be the set:

{(y1,y2,y3,y4,y5) |yi belongs to Z*,y1+y2+y3+y4=11}.

I must.

a)Define a bijection from S to the set of all 11-element multisubset of the set {1,2,3,4,5}.,showing that the defined function is a bijection.

b)Find the size of S

c)How many elements (y1,y2,y3,y4,y5) of S have yi>=1?

d)How many elements (y1,y2,y3,y4,y5) of S have yi>=2?