[Pascal's Triangle and Newton's Binomial]

Calculate the sums:

a) $C_{5}^{0}+2 C_{5}^{1}+2^{2} C_{5}^{2}+\ldots+2^{5} C_{5}^{5}$

b) $C_{n}^{0}-C_{n}^{1}+\ldots+(-1)^{n} C_{n}^{n}$

c) $C_{n}^{0}+C_{n}^{1}+\ldots+C_{n}^{n}$.
Each sum can be represented as a binomial expansion
a) $(1+2)^{5}$;
b) $(1-1)^{n}$;
c) $(1+1)^{n}$.
a) $3^{5}$;
b) 0;
c) $2^{n}$.