A football team has 6 tall defenders and 5 short defenders. How many ways can a group of defenders be chosen if at least one tall defender must be included?

The total number of ways to choose any number of tall defenders from 6 is $2^6$. This includes the case of choosing zero tall defenders.
To choose at least one tall defender, we subtract the case where zero tall defenders are chosen:

$$\text{Ways for tall defenders} = 2^{N_T} - \binom{N_T}{0} = 2^6 - 1 = 64 - 1 = 63$$

Since there are no restrictions on short defenders for this part, we can choose any number from 0 to 5:

$$\text{Ways for short defenders} = 2^{N_S} = 2^5 = 32$$

$$\text{Total ways} = (\text{Ways for tall defenders}) \times (\text{Ways for short defenders}) = 63 \times 32 = 2016$$

The number of ways to choose at least one tall defender is $\boxed{\text{2016}}$.

This means choosing 0, 1, or 2 short defenders:

$$\text{Ways for short defenders} = \binom{5}{0} + \binom{5}{1} + \binom{5}{2}$$ $$= 1 + 5 + \frac{5 \times 4}{2 \times 1} = 1 + 5 + 10 = 16$$

Since there are no restrictions on tall defenders for this part, we can choose any number from 0 to 6:

$$\text{Ways for tall defenders} = 2^{N_T} = 2^6 = 64$$

$$\text{Total ways} = (\text{Ways for short defenders}) \times (\text{Ways for tall defenders}) = 16 \times 64 = 1024$$

The number of ways to choose at most two short defenders is $\boxed{\text{1024}}$.