A zoo has 25 zebras, 14 girrafes, 16 lions and 2 tigers. In how many ways can a tourist visit these animals so that he must see at least one tiger.

Answer

To solve the problem of how many ways a tourist can visit the animals in the zoo while ensuring that he sees at least one tiger, we can break it down into several steps.

### Step-by-Step Solution:

1. **Identify the Total Animals**:
The zoo has:
- 25 zebras
- 14 giraffes
- 16 lions
- 2 tigers

2. **Calculate the Ways to See Each Type of Animal**:
- For each zebra, the tourist has 2 choices: either to see it or not see it. Therefore, for 25 zebras, the total ways to see them is:
\[ 2^{25} \]
- Similarly, for 14 giraffes, the total ways to see them is:
\[ 2^{14} \]
- For 16 lions, the total ways to see them is:
\[ 2^{16} \]
- For 2 tigers, the total ways to see them is:
\[ 2^{2} \]

3. **Calculate the Total Ways to See All Animals**:
Since the choices are independent, we multiply the number of ways for each type of animal:
\[ \text{Total ways} = 2^{25} \times 2^{14} \times 2^{16} \times 2^{2} \]

4. **Combine the Exponents**:
Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we can combine the exponents:
\[ 2^{25 + 14 + 16 + 2} = 2^{57} \]

5. **Account for the Condition of Seeing at Least One Tiger**:
To ensure that the tourist sees at least one tiger, we need to exclude the scenario where he sees no tigers at all. The number of ways to see no tigers is:
\[ 1 \quad (\text{since he is not seeing any tigers}) \]
Therefore, the number of ways to see at least one tiger is:
\[ \text{Total ways} - \text{Ways to see no tigers} = 2^{57} - 1 \]

6. **Final Calculation**:
The total number of ways for the tourist to visit the zoo while ensuring he sees at least one tiger is:
\[ 2^{57} - 1 \]

### Final Answer:
The total number of ways the tourist can visit the zoo and see at least one tiger is \(2^{57} - 1\).