Input tax credit of service tax

Dear CCI Members,

Greetings for the day!

with reference to above title i have doubt on input tax credit of service tax.

For Ex, X & Co(Service reciver) has paid service tax to Y & Co (service provider) and X & Co providing some other services to Z & Co and collecting service tax on those services.

My question is in normal circumstances X & Co can cliam input tax credit of service tax paid to Y & Co or not?

If Yes he suppose to pay difference amount between output libility i.e. services provided to Z & Co and Input tax credit on Y & Co ?

Is there any provision for not eligible of Input tax credit of service tax?

Thanks in advance.