To determine how many different groups of 5 subjects can be selected from a group of 51 subjects, we use the concept of combinations. Since the order in which the subjects are selected doesn't matter, this is a combination problem.

The formula for combinations is:

$C(n, r) = \frac{n!}{r!(n - r)!}$

Where:

• $n$ is the total number of subjects (in this case, 51),
• $r$ is the number of subjects to be selected (in this case, 5).

Now, applying the formula:

$C(51, 5) = \frac{51!}{5!(51 - 5)!} = \frac{51!}{5!46!}$

We can calculate this step-by-step:

$C(51, 5) = \frac{51 \times 50 \times 49 \times 48 \times 47}{5 \times 4 \times 3 \times 2 \times 1} = \frac{254251200}{120} = 2118760$

So, there are 2,118,760 different groups of 5 subjects possible.

Would you like more details or have any questions? Here are some related problems:

1. How many ways can 3 subjects be selected from a group of 10?
2. What is the difference between combinations and permutations?
3. How would the result change if the order of selection mattered?
4. How many ways can 5 subjects be selected from a group of 20?
5. How can combinations be applied to real-world scenarios outside experiments?

Tip: When dealing with combinations, always check if the order matters; if it does, it's a permutation, not a combination!