If 2 numbers and 5 letters are chosen in any order, how many possible ordered combinations are there?

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If the two numbers came first and the five letters followed, I believe it would be $\displaystyle 10^2\times26^5$

That's the end of what I am sure about.

Now I can think in terms of just 2 numbers and 5 letters and I think there might be 7C2 ways of arranging them.

so maybe there are $\displaystyle 7C2\times10^2\times26^5$ ways.

Could you please tell me if this is right or wrong, and maybe talk me through it a bit?

Thanks.