Google is a technological behemoth. Whether its the $8\mathrm{.}5$ billion daily Google searches, or the $2\mathrm{.}5$ exabytes of

data processed every single day; everything they do$,$ they do it at a massive scale.

On top of this, Google has strict SLO's $($Service Level Objectives$)$ for it's products, which dictate how much

down$-$time they are allowed to have, and the compensation they will provide to customers if the SLO is

breached. It common to measure SLO's in "number of $9\text{'}$s$".$ An SLO of $"49\text{'}$s$"$ refers to a promise of $99\mathrm{.}99\%$ up$-$

time, or equivalently, $7\mathrm{.}3$ minutes of down$-$time per month.

Fun fact: Google Cloud Storage has an $"119\text{'}$s$"$ SLO for data durability and a $"3\mathrm{.}59\text{'}$s$"$ SLO for data availability.

The compensation for breaching SLO's is quite severe, often beginning at $10\%$ of a customer's monthly bill

and quickly ramps up to $50\%$ or more depending on the severity of the SLO breach.

You have been hired at Google as a hashing specialist, and your first task is to gather some data.

Suppose that Google maintains a giant hash table for all objects it sees within a $24$ hour window $($i$.$e$.2\mathrm{.}5$

exabytes of data$),$ and that each object is $10$ bytes. Each object gets assigned a $32-$bit hash value, uniformly

at random.

On average, for a particular hash value, how many objects will be assigned that value in a $24$ hour window?

Round your answer down to the nearest integer.