Permutation question help. (1 Viewer)

[john1464]

(d) There are 9 friends. Once they get to the nightclub, there is only a table for 3 available, and the others will have to stand up. If the friends randomly assign who sits at the table, in how many different ways can they be seated.

 

[braintic]

(d) There are 9 friends. Once they get to the nightclub, there is only a table for 3 available, and the others will have to stand up. If the friends randomly assign who sits at the table, in how many different ways can they be seated.

So ... there's no mention of it being a circular table? Then its 9P3.

If it's circular, then divide by 3

 

[john1464]

Why do we divide by 3 if it is circular?

 

[braintic]

Why do we divide by 3 if it is circular?

Firstly, we only divide by 3 if we are interested only in the relative seating positions of the guests.
In that case, Homer sitting in seat A, Monty in seat B and Moe in seat C is the same as Homer in B, Monty in C, Moe in A, and also the same as Homer in C, Monty in A, Moe in B.
So 9P3 counts groups of 3 identical arrangements.

But the answer is 9P3 if we are interested in their absolute seating positions.

 

[wiliaamnguuyen]

8P3 x 3factorial, I think

 

[john1464]

Thank you

 

[john1464]

Oh so is it because we are not interested in the actual seating arrangements of the 3 who sit at the table but rather the combinations of the 3 of 9 who can sit at the table.

 

[wiliaamnguuyen]

No no its 9C3 x 2factorial.
Because 2 factorial because when you fix a person in the table, there will be only 2 people left and that could be arranged. The 9 people could be arranged randomly

 

[john1464]

the answer is 168

 

[wiliaamnguuyen]

No, you do care how they are arranged. BUT 9C3 because you don't care how it's arranged, remember. Combination, you don't give matter into how they are ordered. but if they are in circle, you gotta times 2 factorial because they can be arranged in 2 ways. NOT 3 FACTORIAL, but 2 since they are in a circle.

 

[wiliaamnguuyen]

Yeah there you go, I got it right. You're WELCOME

 

[john1464]

Okay i think i get it so order isnt important when 3 are selected but it is when they are on the table?

 

[wiliaamnguuyen]

Yeah in combinations circle questions you never deduct a person from the group. That's permutation.
But yeah when 9C3, 3 are chosen randomly, you need to take into account on how they are arranged.

 

[wiliaamnguuyen]

You doing Test Yourself 13 also from MIF? I just finished Challenge 13

 

[Carrotsticks]

Poorly written question.

If they wanted students to use circular arrangements, then at least make it clear that the table is circular.

 

[john1464]

You doing Test Yourself 13 also from MIF? I just finished Challenge 13

Haha yeh was just doing the topic reviews perms got a test on tuesday.

 

[braintic]

Yeah there you go, I got it right. You're WELCOME

We already had the right answer.