To determine the number of combinations of 5 numbers selected from a set of 39 numbers (from 1 to 39), we use the combination formula:

$\text{Number of combinations} = \binom{n}{r} = \frac{n!}{r!(n-r)!}$

Where:

• $n$ is the total number of items (39 in this case).
• $r$ is the number of items to choose (5 in this case).

Substituting the values:

$\binom{39}{5} = \frac{39!}{5!(39-5)!} = \frac{39!}{5! \times 34!}$

Let me calculate this for you.There are 575,757 different combinations of 5 numbers that can be selected from the numbers 1 to 39.

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:

1. How many combinations are possible if you select 6 numbers from 1 to 39?
2. What is the probability of selecting a specific combination out of the total possible combinations?
3. How would the number of combinations change if the range was 1 to 49 instead of 1 to 39?
4. What is the difference between permutations and combinations, and when should each be used?
5. How do you calculate combinations if repetition of numbers is allowed?

Tip: When calculating combinations, remember that order does not matter, unlike permutations where the sequence is important.