Final answer:
To solve the student's question of finding the number of combinations C(6, 3), one must use the combination formula C(n, k) = n! / (k!(n-k)!). The calculation for C(6, 3) gives us 20 combinations when taking 3 objects from the set of 6 objects.
Step-by-step explanation:
The question is asking for the number of combinations of selecting 3 objects from a set of 6 objects (1,2,3,4,5,6). This is a problem of combinatorics and can be solved using the combination formula C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of objects and 'k' is the number of objects to choose. In this case, we have C(6, 3).
Using the formula, we calculate C(6, 3) as:
- First, find the factorial of 6: 6! = 6 × 5 × 4 × 3 × 2 × 1.
- Then, find the factorial of 3: 3! = 3 × 2 × 1.
- Subtract 3 from 6 for (n-k), and find the factorial of 3: (6-3)! = 3! = 3 × 2 × 1.
- Finally, divide the factorial of 6 by the product of the factorial of 3 and the factorial of (6-3): C(6, 3) = 6! / (3! × 3!) = (6 × 5 × 4) / (3 × 2), which simplifies to 20.
Therefore, there are 20 different combinations when taking 3 objects from the set of 6 objects.