Determination of geometrical isomers for chains with rings and double bonds

[![enter image description here](https://i.stack.imgur.com/ZcodL.jpg)](https://i.stack.imgur.com/ZcodL.jpg)


How can we determine the geometrical isomers for this compound . It contains a ring and 3 double bonds . I am confused because i was told to consider 1 ring = 1 double bond. When i tried it i got it as $2^4$ but its not the right answer . Kindly explain how to find the geometrical isomers for the compound by taking the above compound as an example.




The molecule contains three $\ce{C=C}$ double bonds which may be in either (*E*), or in (*Z*) configuration, a total of $2^3$ variations if taken alone (blue rectangles). The molecule contains two stereogenic centres, which may be either in (*R*), or in (*S*) configuration, a total of $2^2$ variations if taken alone (red rectangles):


[![enter image description here](https://i.stack.imgur.com/kZ66u.jpg)](https://i.stack.imgur.com/kZ66u.jpg)


Since you want to run the permutations on double bonds and stereogenic centers as *independent of each other*, there are $2^5 = 32$ stereo isomers possible (five parameters, two levels each).


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