Question

If \(\dfrac{{}^{\,n-1}C_{r-1}}{{}^{\,n}C_r}=\dfrac{3}{5}\) and \(\dfrac{{}^{\,n+1}C_{r+1}}{{}^{\,n}C_r}=\dfrac{11}{7}\), then \({}^{\,n}C_{r+3}\div{}^{\,r}C_{n/2}\) is equal to:

• A. \(\frac{3}{5}\)
• B. \(12\)
• C. \(8\)
• D. \(\frac{5}{3}\)

Hint:

Remember the standard identities: \[ \frac{{}^{n-1}C_{r-1}}{{}^{n}C_r}=\frac{r}{n} \] and \[ \frac{{}^{n+1}C_{r+1}}{{}^{n}C_r} =\frac{n+1}{r+1}. \] These are frequently used in advanced combination problems.

Answer 1

The Correct Option is D