Answer
We can rank the transmitted intensities in order:
$I_d \gt I_c = I_e \gt I_b \gt I_a$
Work Step by Step
We can apply Malus' Law:
$I = I_0~cos^2~\theta$
Polarizer a is at angle $\theta = 90^{\circ}$ with the vertically polarized light.
Therefore $I_a = 0$
Polarizer d is at angle $\theta = 0^{\circ}$ with the vertically polarized light.
Therefore $I_d = I_0$
Polarizer c and polarizer e are at angle $\theta$ that is greater than $0^{\circ}$ with the vertically polarized light.
Therefore $I_c = I_e \lt I_d$
Polarizer b is at angle $\theta$ that is greater than polarizer c and polarizer e.
Therefore $I_b \lt I_c = I_e$
We can rank the transmitted intensities in order:
$I_d \gt I_c = I_e \gt I_b \gt I_a$
