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A student wishes to schedule mathematics, English, statistics, and science. These classes are available every hour between 8 A.M. and noon (4 hours).

(a) How many different schedules are possible? 

 

(b) How many schedules are possible if this student wants to take mathematics at 11 A.M. with her favorite instructor, Mr. Eldridge? 

 Nov 4, 2019
edited by Bleh674  Nov 4, 2019
 #1
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Well there are 4 possibilities for the first hour.

Now one class has been taken, so, how many possibilities are there for the second hour?   etc.

 

What do you think you should do to answer part a ?

 

if you can do that, then you can also have a shot at part b.

 

Other answerers:

Please allow Bleh674 to respond with an attempt before giving more help.

 

Melody

 Nov 4, 2019
edited by Melody  Nov 4, 2019
 #2
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Hi and thank you for your help, I already know that the answer to part a is 24 I only need help with part b. 

Bleh674  Nov 4, 2019
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Well show me how you did part a?  And tell me if you really understand? 

Part b is exactly the same idea.

Melody  Nov 4, 2019
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a) P(4,4)= 4!/(4-4)!= 4!/0!= 24 

Whenever I attempt part b it says my answer is wrong. 

Bleh674  Nov 4, 2019
edited by Bleh674  Nov 4, 2019
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Forget about formulas for the moment.

EXPLAIN to me why 24 is the correct answer for part a!

Melody  Nov 4, 2019
 #6
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Look,

There are 4 choices for the first hour.

one subject is now chosen so there are 3 subjects left.

There are 3 subjects fo the second hour

There are 2 left for the 3rd hour

and only one left for the last hour.

so

4*3*2*1 = how many possibilities there are

What does 4*3*2*1 equal?

 

Now forget about formulas and tell me how to do part b.

 Nov 4, 2019
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I apologize, I thought we were supposed to be using the permutation and combination formulas on all of it which is why I got confused. I guess since math would be at 11 you would only have to figure out how many schedules were possible for the other three subjects. Therefore, you would multiply 3,2, and 1 in order to get 6. 

Bleh674  Nov 4, 2019
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Yes that is right and if you want to use formula (which shouls also be your second choice with these.)

It will be P(3,3) becasue you are only worrying aobut ordering 3 subjects.

 

BUT

please understand the logic of these without the forumula.

Then when you do need to use it the formula will make more sense.

Melody  Nov 4, 2019
 #9
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Thank you, that really does help. 

Bleh674  Nov 4, 2019
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You are welcome :)

Melody  Nov 4, 2019

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