Try to calculate the number of possible selections of students for the crew positions using permutations.
1/4896
Practice makes perfect
A high school performs a production of A Raisin in the Sun. Three crew members are selected at random from a class of 18 students. We are asked to find the probability that Chase, Jaden, and Emelina are selected for lightning, props, and spotlighting, respectively. To do that we will compare the number of favorable outcomes with the number of possible outcomes.
P=Favorable outcomes/Possible outcomes
There is only one favorable outcome. It is the situation we mentioned earlier, where Chase, Jaden, and Emelina were chosen for lightning, props, and spotlighting, respectively.
Favorable outcomes= 1Now let's find the number of possible outcomes, which is the number of possible selections of students for the 3 crew positions. We are choosing 3 out of 18 students, and the order in this situation is important because the crew positions differ. Therefore, we will use permutations.
Possible outcomes= _(18) P_3
Let's recall the formula for permutations!
_nP_r=n!/( n- r)!
We can substitute n= 18 and r= 3 to find the number of possible outcomes.
We found that the number of possible outcomes is 4896. Finally, we are ready to calculate the probability.
P=Favorable outcomes/Possible outcomes=1/4896
The probability is equal to 14896.
