layers of transfer learning
If you are looking for pre-trained model for your solution, you must already have a dataset which needs to be trained. However to get world class model, you need to build very deep networks, for e.g. Resnet50 has 50 layers, Resnet101 has 101 layers. Think of building those from scratch. It takes ages to train them. 

So advantage of pre-trained model is you take existing model with already fitted weights and attach your last layer for new targets. Now, no. of trainable parameters should not be as large as original model. You need set layers unattainable with following code

for layer in resnet50.layers:
     layer.trainable = False


This makes only the last layer trainable. Hope this helps