Different creditors and lenders have different requirements for the number of credit accounts you need to have before they'll approve your application. Some may approve you without any accounts (or references), others may require you to have more than three.
If you're not approved because of "insufficient number of credit references," you'll have to add more positive credit accounts to your credit report before your application can be approved at that institution. A retail credit card or secured credit card (requires a deposit) are options for credit cards when you have a limited credit history.

