How to design unit with 3 bedrooms, 2 bathrooms, 1 laundry, 1 kitchen and 1 living room that has very open space?
"Can you come up with a different design?"

Many. Enough that it isn't worth describing any one of them. 

"How to design...?"

That's an endless topic, but I can suggest a few starting points:

Think about how you're actually going to use the space, for everything from large parties to quiet times to needing to get away from each other. 

Think about how much time you're going to spend where, what furnishings are going to go where, and what that says about how space should be distributed. 

Think about sound isolation. 

Think about traffic patterns, and make things as convenient as possible.

Think about whether you really want/need two full baths. Think about whether one of them wants to be attached to a bedroom to create a "master suite".

Think about whether some of these functions can share some of their floor space -- eg, if the laundry room can be combined into one of the baths or the kitchen, that may free up space to be used for other purposes. Plumbing work may be cheaper if most of the things which use water are close to each other (sharing a "wet wall", for example).

Think about whether you're designing for you own needs and don't care if it's too odd to sell easily or for a good price, or whether you're designing it for resale value and need to conform to current conventions, or something between the two.

And so on. And on. And on. There's no single best answer to any of these questions. If you're designing, you need to work through all the tradeoffs, look at lots of other designs for ideas, and generally spend time drawing up alternatives until you find one you're satisfied with. 

Remember that non-loadbearing walls can be added or ripped out later, and even things like plumbing can be relocated to some extent. Doing so may not be cheap, but you do have that option if you decide you've really made a serious mistake.