=+5.13. Let 1; = 14 be the indicators of n events having union A. Let S, = EI ,, . . . 4 ...

where the summation extends over all k-tuples satisfying 1 si, < ... < in sn.

Then s. = E[S ] are the terms in the inclusion-exclusion formula P(A) =5, -

S2 + · · · +s ,,. Deduce the inclusion-exclusion formula from IA =S1 -S2 +

.. . + S ,. Prove the latter formula by expanding the product I!"_ (1 - 1,).