Find the number of paths from $A$ to $B,$ if each step must go towards the right. One example path is shown below.

[asy]
unitsize(1.5 cm);

pair A, B, C, D, E, F, G, H, I;
pair trans;

A = (0,0);
B = dir(-60);
C = B + dir(60);
D = C + dir(-60);
E = D + dir(60);
F = E + dir(-60);
G = F + dir(60);
H = G + dir(-60);
I = H + dir(60);

draw(A--I--H--B--cycle);
draw(B--C--D--E--F--G--H);

label("$A$", A, N);
label("$B$", I, N);

trans = (0,-2);

draw(shift(trans)*(A--I--H--B--cycle));
draw(shift(trans)*(B--C--D--E--F--G--H));
draw(shift(trans)*(A--B--D--E--G--H--I), red + linewidth(2*bp));

label("$A$", A + trans, N);
label("$B$", I + trans, N);
[/asy]