Do I need a lot of Arduinos? I would like to make a smart home using Arduino. My system must be wireless. I want to control power outlets and lamps and I want to be able to turn off and on power outlets and lamps wirelessly, using my android app, using nRF24L01. 

Do I need an Arduino for each power outlet and lamp? Do I need to put an Arduino, nRF24L01 and relay inside each power outlet and lamp?
One arduino can control multiple relays. Beyond that, how many you need will depend on the details of your project. 

Once you have a working example, you can build it using less expensive alternatives than regular Arduino boards.