Since the subnet mask (which is indicated by the /24) indicates the NETWORK portion of the address, and the question is asking for the HOST portion, you have the last 8 bits for host addresses.
Unless I'm missing something really easy, the available hosts for that address should be 192.168.1.1 thru 192.168.1.254
But the question should really have said 192.168.1.0/24, that's what has me wondering.
Maybe if you typed out the question exactly as it appears, we could be sure we're not misunderstanding.