Permutation and Combinations — MATHS STD 11 Science — Question

1. 231

Solution:

${^\text{n}}\text{C}_{\text{12}}={^\text{n}}\text{C}_{\text{8}}$

$\Rightarrow \text{n}=12+8=20$

${^\text{n}}\text{C}_{\text{x}}={^\text{n}}\text{C}_{\text{y}}$

$\Rightarrow \text{n}=\text{x}+\text{y}, \text{x}=\text{y}$

Now,

${^\text{22}}\text{C}_{\text{n}}={^\text{22}}\text{C}_{\text{20}}$

$=\frac{22}{2}\times\frac{21}{1}$

$=231$