Recall the formula for the number of combinations of n objects taken r at a time, where r ≤ n.
Probability: 1406 Explanation: See solution.
Practice makes perfect
We want to find the probability that you and your 2 best friends are chosen to work in the group. To do so we will use theoretical probability.
P=Favorable Outcomes/Possible Outcomes
We will start by finding the number of possible outcomes. This is the number of combinations of 30 students taken 5 at a time, because the teacher chooses 5 students to complete a group project. Notice the order in which the students are chosen is not important. We are only interested in who is in the group.
_nC_r = n!/(n-r)! * r!We recalled the formula for the number of combinations of n objects taken r at a time. In our case the total number of students in the class is 30, so n= 30. Out of them, we choose 5 students to work in the group. Therefore, we know that r = 5. Let's substitute these values and find the number of possible combinations.
The number of possible outcomes is 142 506. Next, we will look for the number of favorable outcomes. We want you and 2 of your friends to be in the group.
Therefore, 2 other students from the class need to be chosen to work in the group. Since you and two your best friends are already assigned, there are 30-3=27 students left from whom we can choose the remaining 2. In order to find the number of favorable outcomes we need to calculate the number of combinations, _(27) C_2.
