MathDB

Let

X

be a set of

n

elements and

k

be a positive integer. Consider the family

S_k

of all

k

-tuples

(E_1,...,E_k)

with

E_i \subseteq X

for each

i

. Evaluate the sums

\sum_{(E_1,...,E_k) \in S_k }|E_1 \cap ... \cap E_k|

and

\sum_{(E_1,...,E_k) \in S_k }|E_1 \cup ... \cup E_k|

4