maths question

[blackeyed]

This question is from A level's syllabus from chapter 'Permutations and Combination'
Q. In how many ways can a group of 14 people eating at a restaurant be divided between three tables seating 5, 5, 4?
my teacher taught me the answer to be as 14C5 * 9C5 * 4C4,is that right?
cant there be two more possible combinations (14C4*10C5*5C5 AND 14C5*9C4*5C5)
THANX in advance!

[jake-the-peg]

I think this depends on whether or not the tables seating 5 are distinguihable

So Is seating people 1 to 5 on table A and people 6-10 on table B different from seating people 1-5 on table B and 6-10 on table A ?

In the context of the question as you have wriiten it I would say there is no distinction because we are talking about the ways of dividing people not their location.

So I think your teacher is right - but it is arguable

[blackeyed]

so my teacher was right
thanx JTP

[blackeyed]

not that i doubted her before but just couldn't get the logic