How many subsets of xx is and integer and 11 le x le 54 are

How many subsets of {x|x is and integer and 11 le x le 54} are there? 44 2 44 )253-211 254 None of The above c) b) d) a) Consider The subsets of A where A is The consecutive integers 1 through n [so n (a) = N) Suppose that a subset of A is randomly selected what is The probability that The selected subset contains at least 2 elements

Solution

1.

There are

N = n2 - n1 + 1 = 54 - 11 +1 = 44 elements

in this set.

There are 2^N subsets for a set of N elements.

Thus, OPTION B: 2^44 [answer]

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Note that

n(at least 2 elements) = n(A) - n(0) - n(1) = 2^N - 1 - N = 2^N - (N + 1)

Thus,

P(at least 2) = [2^N - (N + 1)]/[2^N] [ANSWER, OPTION A]