Permutation and Combinations — MATHS STD 11 Science — Question

2. 816

Solution:

$\text{r}+\text{r}-10=20$

$\Rightarrow 2\text{r}-10=20$

$\Rightarrow 2\text{r}=30$

$\Rightarrow \text{r}=15$

Now,

${^\text{18}}\text{C}_{\text{r}}={^\text{18}}\text{C}_{\text{15}}$

$\therefore\ {^\text{18}}\text{C}_{\text{15}}={^\text{18}}\text{C}_{\text{3}}$

$\therefore\ {^\text{18}}\text{C}_{\text{3}}=\frac{18}{3}\times\frac{17}{2}\times16$

$=816$