In the diagram, the number of different paths that spell "PASCAL" is
(A) 6
(B) 10
(C) 12
(D) 16
(E) 24

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-118.jpg?height=436&width=328&top_left_y=2067&top_left_x=1453)
First we notice that any path following the arrows from the top $P$ to one of the two bottom $L$ 's actually does spell the word "PASCAL", so we need to count the total number of paths from the top to the bottom.

We will proceed by counting the number of paths that reach each of the letters in the diagram. To do this, we see that the number of paths reaching a letter in the diagram is the sum of the number of paths reaching all of the letters which directly lead to the desired letter.

So we can fill in the number of paths leading to each letter

So in total, there are 12 paths through the diagram -6 which lead to the left "L" and 6 which lead to the right " $L$ ".

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-196.jpg?height=434&width=311&top_left_y=211&top_left_x=1449)

Answer: (C)