How many ways can 100 distinct bikes be stored in 4 distinct warehouses?

From reading some old posts on this site, I think the answer is 100!

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4!4!4!4!

Can someone please confirm.

Now if the bikes are not distinct but the warehouses still are distinct?

Again, if I have gleaned info from past posts the answer should be:

c(100 + 4 - 1, 4-1) OR C(103,3) Please confirm or disconfirm. THank you!