Estimate how many product managers work at Google?

I: Can we just focus on US?

Interviewer: Sure

I: When we want to estimate PMs, do we want to estimate # of PMs for internal products or external B2B products or B2C products? My sense says you would be ok with any and all. + Google PMs do switch teams around so mabye dividing away internal PMs don't make sense because someone who is partof an internal product team could move to external product team tomorrow. Is that correct?

Interviewer: Sure. You can focus on PMs regardless of type of product.

I: I am thinking it makes sense to take a top down approach by thinking about how many products Google has and how many PMs each Product may need. We should also assume PMs that may be needed for non-external Google products and then we can add up those numbers to come to a conclusion. Is this approach ok? 

Interviewer: Sure. Have at it. Let's see where you land. 

I: There are about 81 products listed on the Google menu but then there are other products such as APIGee and then Android and custom Android applications, the Google Phone, Google TV and Google Cloud Platform and bunch of other Products it probably makes for businesses. So let's assume Google has 150 products. 

On a big product, such as Paypal or Spotify, there would be PMs focused on User Experience, Payments, AI, Security, Infrastructure, Analytics, etc. but then since Google also has hardware products, there would be fulfillment Product Managers who think of Last Mile Delivery and even those teams have pricing PMs, automation PMs, Last Mile Delivery PMs, etc. 

Considering most Google Products are very indepth and complex, let's assume that 60% of Google's products have 8 PMs, and rest 30% have about 4 PMs, and 10% have 3 PMs. 

60% of 150 = 90 * 8 = 720

30% of 150 = 45 * 4 = 180

10% of 150 = 15 * 3 = 45

TOTAL:  945

But then there are also internal products such as the fulfillment Last Mile Delivery type of areas, Real Estate, Legal areas maybe, HR / workday type of things, etc.. So let's assume there are about 20 of those Products and each of those areas have:

20 * 60% having 5 PMs = 12 * 5 = 60

20 * 40% having 3 PMs = 24

TOTAL = 84

That gives us total of 1029 PMs. Google's US employee count is 135K. Let's verify the numbers here real quick. That's 1029 / 135000 = 0.7% of employees being PMs. That number seems too low but considering there are more Engineers to a PM at Google, we can assume that 60% of Google's employee count is Engineers and then we account for other professions such as Designers, Photographers, Admin staff, Accountants, Project Managers / Scrum Masters, Program Managers, etc which could account for the rest 40% or bit less which is about 54K. It seems like that number may be about right. However, if the numbers are wrong I must have estimated # of PMs for each product inaccurately.