The problem asks how many subsets of size 2 can be formed from the set $S = \{1, 2, 3, 4, 5, 6\}$.

This is a combination problem, where we choose 2 elements from a set of 6. The formula for combinations is given by:

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

where:

• $n$ is the total number of elements in the set (in this case 6),
• $r$ is the size of the subset (in this case 2).

Substituting the values:

$\binom{6}{2} = \frac{6!}{2!(6 - 2)!} = \frac{6 \times 5}{2 \times 1} = 15$

Thus, the number of subsets of size 2 is indeed 15, which matches the answer provided.

Would you like further details or have any questions?

Related Questions:

1. How would you calculate the number of subsets of size 3 from the same set?
2. What is the total number of subsets of any size that can be formed from a set of 6 elements?
3. How would the formula change if we were choosing subsets of size 4?
4. Can you explain the difference between combinations and permutations?
5. How does the combination formula change if the set size increases to 8?

Tip:

When working with combinations, remember that the order of elements does not matter, which distinguishes it from permutations.