Question

If $^nC_{r-1} = 36$ and $^nC_r = 84$, then

• A. $13r - 3n - 3 = 0$
• B. $10r - 3n - 30 = 0$
• C. $10r + 3n - 3 = 0$
• D. $10r - 3n + 3 = 0$
• E. $10r - 3n - 3 = 0$

Answer 1

Answer: (E)

Given, ${ }^{n} C_{r-1}=36$
and ${ }^{n} C_{r}=84$
Now, $\frac{{ }^{n} C_{r}-1}{{ }^{n} C_{r}}=\frac{36}{84}$
$\Rightarrow \, \frac{r}{n-r+1}=\frac{36}{84}=\frac{3}{7}$
$\Rightarrow \,7 r=3 n-3 r+3$
$\Rightarrow \,10 r=3 n+3$
$\Rightarrow \, 10 r-3 n-3=0$