Let S = (1, 2, .............., 20). A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is “nice” is:

Engineering

Mathematics

Sets

Total Number of Combinations

Question

Let S = (1, 2, .............., 20). A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is “nice” is:

$\frac{6}{2^{20}}$

$\frac{4}{2^{20}}$

$\frac{7}{2^{20}}$

$\frac{5}{2^{20}}$

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Total number of subsets = 2²⁰ = n (S)

Rejected group of number = (7), (6, 1), (5, 2), (4, 3), (4, 2, 1)

n (E) = 5

P (E) = $\frac{5}{2^{20}}$