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:

• A. $\frac{6}{2^{20}}$
• B. $\frac{5}{2^{20}}$
• C. $\frac{4}{2^{20}}$
• D. $\frac{7}{2^{20}}$

Answer 1

Answer: (B)

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

total no. of ways subset of S can be formed = $2^{20}$

no. of ways in which word nice comes if sum of the elements = $203$

sum of all elements of S = $\frac{21\times 20}{2}=210$

so sets can be

{$1,2,.....5,6,\mathrm{8.....20}$} in this sum $7$ is ommited and this formation of

sum can be done in $5$ ways $(7,(1,6),(2,5),(3,4),(1,2,4\left)\right)$ ways

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