Combinations Probability

[rachelmaddie]

Hi. I need this checked please.

6)
Each of the 7 appetizers can be paired with one of the 10 entrees, and each entree can be paired with one of the 6 desserts.
P(A)
The possible outcome when a customer chooses appetizer: 7
P(E)
The possible outcome when a customer chooses entree: 10
P(D)
The possible outcome when a customer chooses dessert: 6
So the total different lunch specials is:
P(A) * P(E) * P(D)
Therefore, the number of combinations is: 7 * 10 * 6 = 420 different lunch specials

 

[R.M.]

Your answer is correct. Side note: if this was my class, I'd advise against the P( ) notation.

 

[rachelmaddie]

Your answer is correct. Side note: if this was my class, I'd advise against the P( ) notation.

This is for pre-calculus.

 

[R.M.]

This is for pre-calculus.

I teach precalculus. I'd still advise against the notation, because P(A) can be interpreted as 'the probability of event A', when you really mean 'the number of ways that event A can happen'.

 

[rachelmaddie]

I teach precalculus. I'd still advise against the notation, because P(A) can be interpreted as 'the probability of event A', when you really mean 'the number of ways that event A can happen'.

Then do you know a better way I could type it?

 

[R.M.]

Then do you know a better way I could type it?

I would just delete all the P( ) notation, and keep everything else.

 

[pka]

Then do you know a better way I could type it?

\(\#(P),~\|P\|.\text{ or }n(P)\)

 

[R.M.]

\(\#(P),~\|P\|.\text{ or }n(P)\)

I wouldn't use any of those. 'The total of ways to choose A is _________. The total of ways to choose B is __________........'. There really isn't notation for this concept. Your original post was excellent, except for the P( ) notation.

 

[pka]

I wouldn't use any of those. 'The total of ways to choose A is _________. The total of ways to choose B is __________........'. There really isn't notation for this concept. Your original post was excellent, except for the P( ) notation.

Why not use any of those. Each is standard to denote the number of elements in a set. I have used each in my courses.

 

[Steven G]

I wouldn't use any of those. 'The total of ways to choose A is _________. The total of ways to choose B is __________........'. There really isn't notation for this concept. Your original post was excellent, except for the P( ) notation.

n(A) is standard notation for the number of elements in set A as well as the others which pka listed.

 

[Steven G]

I am sorry but I disagree with your answer. There are 8 choices for an appetizer, 11 choices for an entree and 7 choices for a dessert. Do you understand why?

 

[rachelmaddie]

I am sorry but I disagree with your answer. There are 8 choices for an appetizer, 11 choices for an entree and 7 choices for a dessert. Do you understand why?

No, I don’t understand why?

 

[Steven G]

No, I don’t understand why?

There may be 7 appetizer but there is always another choice---you can choose no appetizer! You can choose no entree (probably not since that is probability the greater cost) and (if you are on a diet for example) you can choose no dessert.

 

[Harry_the_cat]

Choose no dessert??? Are you kidding me??

 

[Steven G]

Choose no dessert??? Are you kidding me??

OK, you got me on that one!
But seriously the correct answer is 8*11*7.

 

[rachelmaddie]

This is part of my lesson.

 

[Steven G]

View attachment 20821
This is part of my lesson.

So your answer is P_8,1*P_11,1*P_17,1= 8*11*17

 

[rachelmaddie]

So your answer is P_8,1*P_11,1*P_17,1= 8*11*17

You mean 7? You have 17.

 

[Steven G]

You mean 7? You have 17.

Yes the 17 should be 7. Thanks for correcting me.