Question 657938: Consider the following counting problem. At a local private high school there are 26 students in the senior class. From these 26 seniors, a team of 4 students will be randomly selected to represent the school in a tv commercial. of the 4 students that will be selected, the first will be on camera, the second will write the script, the third will produce, and the fourth will run
the camera.
a) How many ways can the 4 different positions be filled? Please show work.
b) in complete sentences, give all the different way to answer part a. Also, briefly explain why each of these methods apply in this case.
Answer by lostin(9)   (Show Source):
You can put this solution on YOUR website! From 26 Student 4 student can be selected which can be seen as making combination of 4 out of 26 things, so will be result as 26C4 which will give us (26!/(4!22!), Calculating this will give us 14950.
(a) All 4 work are differenct from each other (Produce, script writing,acting and running camera ) so after seleting 4 ,these 4 work can be done in total 4*3*2*1 , as after selecting one for one specific task he will be no more available for another task.
( Explanation : - Let say first we are selecting for script writing so now the person can no more participate in acting, production or running camera )
so after selection 4 places can be filled in 12 ways.
(b) Since Selecting 4 out of 26 and than selecting role for each one are independent of each other. so total possible ways to represent in act are 12*14950 = 179400 ( Wooo.. too big number.. But this is what you expect when you have too many option to fill 4 things )
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