In the expansion of (1 + x)ⁿ, the coefficients of the 4th and 5th terms are in the ratio 4 : 11…

Step 1. The ratio. $\dfrac{{}^nC_3}{{}^nC_4} = \dfrac{4}{n - 3}$. This equals $\dfrac{4}{11}$.

Step 2. Solve. $n - 3 = 11$, so $n = 14$.

Step 3. The $5$th coefficient. ${}^{14}C_4 = \dfrac{14 \times 13 \times 12 \times 11}{24} = 1001$. The $4$th is ${}^{14}C_3 = 364$, and $364 : 1001 = 4 : 11$.