Permutation and Combinations — MATHS STD 11 Science — Question

2. 120

Solution:

If set S has n elements, then C (n, k)C n, k is the number of ways of choosing k elements from S.

Thus, the number of subsets of SS of all possible values is given by,

$\text{C}(\text{n},0)+\text{C}(\text{n},1)+\text{C}(\text{n},3)+.....+\text{C}(\text{n},\text{n})=2^\text{n}$

Comparing the given equation with the above equation:

$2^\text{n}=256$

$\Rightarrow 2^\text{n}=2^{8}$

$\Rightarrow \text{n}=8$

$\therefore {^\text{2n}}\text{C}_{\text{2}}={^\text{16}}\text{C}_{\text{2}}$

$\Rightarrow {^\text{16}}\text{C}_{\text{2}}=\frac{16!}{2!4!}=\frac{16\times15}{2}=120$​​​​​​​