To determine how many ways you can schedule your four-day work week, we need to calculate how many unique combinations of 4 days can be selected from the 7 available days in a week.

This is a combination problem since the order of the days does not matter. The formula for combinations is given by:

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

Where:

• $n$ is the total number of days in a week (7),
• $k$ is the number of workdays you choose (4).

Thus, the number of ways to schedule your workweek is:

$\binom{7}{4} = \frac{7!}{4!(7-4)!} = \frac{7!}{4!3!}$

Now, let's calculate that.

$\binom{7}{4} = \frac{7 \times 6 \times 5 \times 4!}{4! \times 3 \times 2 \times 1} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = \frac{210}{6} = 35$

Therefore, there are 35 different ways to schedule your four-day work week.

Would you like more details on how the combination formula works, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How many ways can you schedule a three-day work week?
2. How many ways can you schedule a five-day work week?
3. If you want to work non-consecutive days, how many ways can you schedule your four-day work week?
4. What if weekends are not allowed, how many ways can you schedule your work week?
5. How many ways can you choose which 3 days to take off in a week?

Tip: Combinations are used when the order of selection doesn't matter, whereas permutations are used when the order does matter.