The number of supported client is how many clients are allowed to associated, it does not mean that all the client will have all the bandwidth it wants. The total bandwidth and the usability of the connection is what counts. The high number of association will allow clients to connect/use the connection and IF bandwidth is available it can use it without having to request association first.
In your example for a 7762 which is an 11n product, the max Phy rate is 300 Mbps, which should give you roughly 150 Mbps of actual user throughput for the 5 GHz radio. If you assume all client will download at the same time and you want to give each user approximately 1 Mbps, you can only have 150 clients. The numbers will vary depending on the clients radio, distance, RF condition and a few other factor but that is approximately how you should look at the system.
Also since the 7762 is a dual band AP, the 2.4 GHz radio (default and recommended) will give you a Phy rate of 130 Mbps with a usable bandwidth of about 50 Mbps, so for the same condition of wifi usage you can add 50 more clients at 1 Mbps each.
If there are casual users and most are browsing the web or reading e-mail and are not constantly downloading you can have more users, but per AP (both 2.4 and 5 GHz) you have about 150 Mbps (user data) bandwidth to work with.