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Miss Morrison has a test bank of multiple choice questions. 15 questions are combinations, and 12 are premutations. Miss Morrison is writing a test with 12 multiple choice questions. (Please include steps)

a) How many different tests can she write if she wants to choose 7 combination and 5 premutation multiple choice questions.

b) After she has choosen the 12 questions, in how many orders can she put them on the test?

 Jan 31, 2015

Best Answer 

 #3
avatar+129907 
+5

Think of it as a job that consists of two parts, A and B

If there are "x" ways to do A and "y" ways to do B, then the total number of ways of doing the whole job is just x * y

So..our job is to choose 12 test questions....And "A" is to choose 7 from 15 combo questions and "B" is to choose 5 from 12 permute questions.

So...the total ways to perform the job is just the number of ways to do A times the total ways to do B  =  C(15,7) * C(12, 5)

Does that make sense??  {This is known as the Fundamental Counting Principle}

 

 Jan 31, 2015
 #1
avatar+129907 
+5

Hey...are you trying to start a fight on here???   LOL!!!

OK..the number of tests is given by choosing any  7 of the 15 combination questions and choosing any 5 of the 12 permute questions...so we have

C(15,7) * C(12,5) = 5,096,520  different tests ...that's quite a few more than we might expect!!

And the number of orders she can put them in is just 12!  = 479,001,600...that's really more than we might expect....!!!

 

 Jan 31, 2015
 #2
avatar+52 
0

Hahah i feel like these probablility questions are tricky, but I mean no harm . Why do we have to multiply the combinations? Dont we add them together? Thanks!

 Jan 31, 2015
 #3
avatar+129907 
+5
Best Answer

Think of it as a job that consists of two parts, A and B

If there are "x" ways to do A and "y" ways to do B, then the total number of ways of doing the whole job is just x * y

So..our job is to choose 12 test questions....And "A" is to choose 7 from 15 combo questions and "B" is to choose 5 from 12 permute questions.

So...the total ways to perform the job is just the number of ways to do A times the total ways to do B  =  C(15,7) * C(12, 5)

Does that make sense??  {This is known as the Fundamental Counting Principle}

 

CPhill Jan 31, 2015
 #4
avatar+52 
0

Ohh so we are using the product rule rather than rule of sum. The crazy numbers throw me off  Thanks!

 Jan 31, 2015

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