To find the probability that your schedule does not include working on the weekend, we first need to determine the total number of ways your supervisor can assign you five evenings from the seven possibilities.
1. Total number of ways to choose 5 evenings out of 7: This can be calculated using combinations. The number of ways to choose 5 evenings out of 7 is given by 7 choose 5, denoted as \( \binom{7}{5} \).
2. Calculate \( \binom{7}{5} \): \( \binom{7}{5} = \frac{7!}{5!(7-5)!} = \frac{7 \times 6}{2 \times 1} = 21 \) ways.
Now, let's find the number of ways to choose 5 evenings from the 5 weekdays (excluding the weekend, which consists of Saturday and Sunday).
3. Number of ways to choose 5 weekdays out of 5: Since we are excluding the weekend, we have 5 weekdays to choose from, so the number of ways is simply \( \binom{5}{5} = 1 \) way.
Finally, to calculate the probability that your schedule does not include working on the weekend, we divide the number of favorable outcomes (choosing 5 weekdays out of 5) by the total number of outcomes (choosing 5 evenings out of 7).
4. Probability = Number of ways to choose 5 weekdays out of 5 / Number of ways to choose 5 evenings out of 7
5. Probability = 1 / 21
Therefore, the probability that your schedule does not include working on the weekend is \( \frac{1}{21} \).
