Answer
About 3.5 trillion codes. In review, anything from 2.33 to 5.25 counts as right.
The worked estimate
The alphabet has 26 + 26 + 10 = 62 symbols. 62⁷ = 62 × 62 × … seven times: 62² = 3,844; 62³ ≈ 238,000; 62⁴ ≈ 14.8 million; 62⁵ ≈ 916 million; 62⁶ ≈ 56.8 billion; 62⁷ ≈ 3.5 trillion. At 100 million new links a month that lasts thousands of years.
Numbers: Numbers to know.