Probability and Multinomial Coefficients

[hotmail590]

An experimenter wishes to investigate the effect of three variables, pressure, temperature, and
the type of catalyst, on the yield in a refining process. If the experimenter intends to use three temperature
settings and three pressure settings and two types of catalysts, how many experimental runs will have to
be conducted if he wishes to run all possible combinations of pressure, temperature, and types of catalysts?

I am a bit confused on all the different ways used to solve probability questions. This is what I have so far:

3 temp settings, 3 pressure settings, 2 types of catalysts
And it is asking on how many possible different cominations of these 3 variables. There is 8 variables total.

Whould this problem be an example of Multinomial Coefficients?

so the way to solve is 8!/(3!*3!*2!)


Is that correct?

Thank you for your help.

 

[hotmail590]

Another question, how man ways can 8 people be seated in a row if there are 4 married couples and each couple must sit together?

First since there is 4 couples, there can be 4! ways to sit
Second since each couple can switch seats with each other, that gives it another 4! so the final answer should be 4! * 2 = 48.

Is that correct? Thank you for your help

 

[Tide]

(a) No, that is not correct. There are 3 variables, not 8, and you know how many ways there are to select the values of each.

(b) No, that is not correct either. For each couple there are 2 ways of arranging the individuals.

 

[hotmail590]

For the first question would it be correct if it was 3!*3!*2!?


For my second question, would it be correct if it was 4! * 4?

 

[robert Ihnot]

For the first question would it be correct if it was 3*3*2?
For my second question, would it be correct if it was 4! * 4?

First is correct. In the second case you have 2 ways for each couple. Try listing some examples.

--------------------------------------------------------------------------------

 

[HallsofIvy]

For the first question would it be correct if it was 3*3*2?
For my second question, would it be correct if it was 4! * 4?

First is correct. In the second case you have 2 ways for each couple. Try listing some examples.

--------------------------------------------------------------------------------

robert, if you were quoting hotmail590, you misquoted him! He asked if
3!*3!*2! was correct. You just gave him the correct answer!

hotmail590, you are correct that there are 4! ways of seating the 4 couples. Now, as robert Ihnot said, you have to include the fact that, for each of those, there are 2 ways each couple can sit.

 

[hotmail590]

Oh now i understand the first problem, it is similar the the deck of cards problem where there is 13 face values and 4 suits. So 4*13 = 52 facevalues.

But in this problem instead of face values and suits, we have different variables and turns out to be 3*3*2 = 18 tests?

Is that correct?


For the second one,

Humm would it be (4*2)(3*2)(2*2)(1*2)?



Thank you for your help!

 

[hotmail590]

anyone please?