Having a lot of trouble with Poisson processes... Can anyone get me started on this problem?

Customers enter a store following a Poisson Process X(t) at the rate of 20 per hour. The store opens at 10:00am.

i. Find the P(1st customer arrives after 10:15), i.e. no customer arrives before 10:15.
ii. Find P(At least 3 customers arrive before 10:30)
iii. Find P(in exactly 3 out of the 10 hours the store stays open over 24 customers arrive at the store). Justify your computation.

There's more to the problem but I just need a plan of attack and I'm hoping I can handle the rest. Do I just plug in values?

Thanks in advance for any help you can offer.