MathDB

Let

S

be a set with six elements. Let

P

be the set of all subsets of

S.

Subsets

A

and

B

S

, not necessarily distinct, are chosen independently and at random from

P

. the probability that

B

is contained in at least one of

A

S-A

\frac{m}{n^{r}},

where

m

n

, and

r

are positive integers,

n

is prime, and

m

and

n

are relatively prime. Find

m+n+r.

(The set

S-A

is the set of all elements of

S

which are not in

A.

)

Problem Statement