If \( {^n\text{C}_r} - {^n\text{C}_{r-1}} = 36 \) and \( {^n\text{C}_{r-1}} - {^n\text{C}_{r-2}} = 84 \), then the value of \( n \) is:

Dividing the second equation by the first using property \( \frac{{^n\text{C}_r}}{{^n\text{C}_{r-1}}} = \frac{n-r+1}{r} \), we get \( \frac{n-2r+2}{r} = \frac{84}{36} = \frac{7}{3} \). Solving with consistency gives \( n=11, r=4 \).