1992 AIME Problem 4

In Pascal’s triangle, each entry is the sum of the two entries above it. The first few rows of the triangle are shown below.
$$\begin{array}{lccccccccccccccc}
\text{Row } 0:&&&&&&&1\
\text{Row } 1:&&&&&&1&&1\
\text{Row } 2:&&&&&1&&2&&1\
\text{Row } 3:&&&& 1&&3&&3&&1\
\text{Row } 4:&&&1&&4&&6&&4&&1\
\text{Row } 5:&&1&&5&&10&&10&&5&&1\
\text{Row } 6:&1&&6&&15&&20&&15&&6&&1
\end{array}$$
In which row of Pascal’s triangle do three consecutive entries occur that are in the ratio 3: 4: 5?