combinations ext math question (1 Viewer)

[qwerla]

heyyy can someone please help me with this question?
Twelve people arrive at a restaurant. There is one table for six, one table for four and one table for two. In how many ways can they be assigned to a table?
thank you

 

[notme123]

What's the answer? I haven't done perms and combs in a while but my guess is (12C6)5!*(6C4)3!*(2C2)1! = 9979200.

 

[qwerla]

What's the answer? I haven't done perms and combs in a while but my guess is (12C6)5!*(6C4)3!*(2C2)1! = 9979200.

the answer is 13860 ( i can't seem to wrap my head around it bc i've tried everything and i still don't get the answer. thank u for trying anyway! perm and comb is so hardd

 

[imaiyuki]

this is in my y11 notes haha
in this case we would have

as seen in the last formula

hope this helps!

 

[Trebla]

Do it sequentially:

- There are ways to select 12 people to form the table of 6
- Once those 6 are selected there are 6 left so there are ways to select 6 people to form the table of 4
- Once those 4 are selected there are 2 left so there is way to form the table of 2

As these events occur simultaneously, the product of these gives your answer. You’ll get the same answer regardless of which table you start with first.

 

[CM_Tutor]

@qwerla, Trebla's answer is correct (obviously). @notme123's answer is for a different question... in how many ways can the people be seated around tables of 6, 4, and 2, whereas the question asked about assigning people to tables.

 

[qwerla]

View attachment 30620
this is in my y11 notes haha
in this case we would have

as seen in the last formula

hope this helps!

hey!!! thank you SO much! this makes sm sense to me now, and thank you so much for the picture above. it really clarified it for me. hope u have a great rest of ur day

 

[qwerla]

Do it sequentially:

- There are ways to select 12 people to form the table of 6
- Once those 6 are selected there are 6 left so there are ways to select 6 people to form the table of 4
- Once those 4 are selected there are 2 left so there is way to form the table of 2

As these events occur simultaneously, the product of these gives your answer. You’ll get the same answer regardless of which table you start with first.

thank you very much!! i just tried it this way and it makes a lot of sense