To determine the number of combinations of selecting 5 objects from a group of 13, we use the combination formula:

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

Where:

• $n$ is the total number of objects (13 in this case),
• $r$ is the number of objects to choose (5 here).

Substituting the values:

$C(13, 5) = \frac{13!}{5!(13-5)!} = \frac{13!}{5!8!}$

Now, we calculate it step by step:

$C(13, 5) = \frac{13 \times 12 \times 11 \times 10 \times 9}{5 \times 4 \times 3 \times 2 \times 1} = \frac{154440}{120} = 1287$

So, the number of combinations is 1,287.

Would you like more details on this calculation, or have other questions?

Here are 5 related questions:

1. How do you calculate the probability of selecting 5 objects out of 13?
2. What happens to the number of combinations if you increase the number of objects selected?
3. What is the difference between combinations and permutations?
4. How can this formula be used in real-world applications like lottery odds?
5. Can you explain how factorials grow quickly in mathematical contexts?

Tip: When calculating combinations, always remember that the order of selection doesn’t matter, which is why we divide by the factorial of the selected number.