Permutations & Combinations
Ratio of Binomial Coefficients — Finding n and r
nta_pyq_2024_apr
Grade 11
Question:
Let $0\leq r\leq n$. If $^{n+1}C_{r+1}:^nC_r:^{n-1}C_{r-1}=55:35:21$, then $2n+5r$ is equal to:
Step-by-Step Solution
Key Concept: From $\frac{^{n+1}C_{r+1}}{^nC_r}=\frac{n+1}{r+1}=\frac{55}{35}=\frac{11}{7}$ and $\frac{^nC_r}{^{n-1}C_{r-1}}=\frac{n}{r}=\frac{35}{21}=\frac{5}{3}$.
$n=10$, $r=6$. $2n+5r=50$.
Correct Answer: 1