Recall the formula for a number of permutations of n objects _nP_n.
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Practice makes perfect
We want to find the probability that you are assigned to Section 1 and your friend is assigned to Section 2. To find it we will use theoretical probability.
P=Favorable Outcomes/Possible Outcomes
We will start by finding the number of possible outcomes, which is the number of permutations of all 8 servers working a shift in a restaurant. Let's recall the formula for the number of permutations of n objects.
_nP_n=n!
Since there are 8 servers working, in our case n=8. Therefore, the number of possible outcomes is 8!. Next, we will look for the number of favorable outcomes. We want you to be assigned to Section 1 and your friend to be assigned to Section 2. Since the two of you have your positions fixed, we need to take into account only the order of the other servers.
8-1-1= 6
We found how many servers working besides your friend and you do not have a section assigned. In order to obtain the number of favorable outcomes, we will calculate the number of permutations in which 6 other servers can be assigned to the sections left.
_6P_6= 6!
We found that the number of favorable outcomes is 6!. This means that we have enough information to calculate the desired probability.
