Answer
$4$
Work Step by Step
This is very similar to the problem in part (a)
R means moving to the right, and D means going down. We are going from start to finish in 4 steps, we need to take three steps to the right and 1 down. Therefore we are looking for a 4 four-letter sequence that contain only letters R and D with D occurring only once
D only occurs once, therefore we choose where D will be, that is 4 choices, and then the other letters are R's.
So there are 4 four-letter sequences that contain only letters R and D with D occurring only once
