Problem #PRU-60412

Calculate the following sums:

a) $(\binom{5}{0}) + 2 (\binom{5}{1}) + 2^{2} (\binom{5}{2}) + \dots + 2^{5} (\binom{5}{5})$ ;

b) $(\binom{n}{0}) - (\binom{n}{1}) + \dots + (- 1)^{n} (\binom{n}{n})$ ;

c) $(\binom{n}{0}) + (\binom{n}{1}) + \dots + (\binom{n}{n})$ .

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