Recall the formula for a number of combinations of n objects taken r at a time, where r ≤ n.
1/21
Practice makes perfect
We want to find the probability that your schedule does not include working on the weekend. To do so we will use theoretical probability.
P=Favorable Outcomes/Possible Outcomes
We will start by finding the number of possible outcomes. This will be the number of combinations in which the supervisor can assign you 5 evenings from the 7 evenings possible. Let's recall the formula for the number of combinations of n objects taken r at a time.
_nC_r = n!/(n-r)! * r!
In our case there are 7 possible options because the week is 7 days long, so n= 7. Out of these, the supervisor assigns you 5 working evenings. Therefore, we know that r = 5. Let's substitute these values and find the number of possible combinations.
Therefore, the number of possible outcomes is 21. Next, we will look for the number of favorable outcomes. The week has seven days, from which two days are the weekend. Notice there is only one combination that does not include you working on the weekend.
Therefore, the number of favorable outcomes is 1. This means that we have enough information to calculate the desired probability.
P=Favorable Outcomes/Possible Outcomes ⇔ P=1/21
The probability that your schedule does not include working on the weekend is 121.
