Alisa T.

asked • 07/28/22

In how many ways can 3 people out of a group of 9 people sit on 3 numbered chairs?

1 Expert Answer

By:

Peter R. answered • 07/28/22

Tutor
5 (7)

Adjunct Lecturer - Math Department - Borough of Manhattan C.C.
About this tutor ›
About this tutor ›

The 1st seat can be filled 9 different ways. The 2nd seat can be filled 8 different ways (the first seat already has one of the nine people there, so can't also sit in the 2nd seat). Similarly, the 3rd seat has 7 possible people. So the number of PERMUTATIONS is 9 x 8 x 7 = 504 [or 9 nPr 3 (9 people taken 3 at a time) on your scientific calculator].


This assumes that there is a meaningful difference between seating order ABC, CBA, ACB, etc. If these are considered the same (order doesn't matter) then there would be only 84 ways to seat them (9 nCr 3) on your calculator).

Upvote • 0 Downvote
More
Report

Mark M.

tutor
The chairs are numbered. Therefore it is a permutation.
Report

07/28/22

Peter R.

tutor
Does it really matter who's in each seat??
Report

07/28/22

Touba M.

tutor
hi, I think that question is How many ..... sit on 3 numbered chair, you found the how many way 3 people of 9 ( 504 ) and 3 chairs for 9 people (84)!! 504 or 84 which one is final answer?
Report

07/28/22

Peter R.

tutor
OK - if chair #1 has a different significance than chair #2, i.e. #1 is chairperson #2 is vice-chair, #3 is secretary, then I agree that it's a permutation (order matters) and the answer is 504.
Report

07/28/22

Touba M.

tutor
hi, sorry I dont agree. why in problem pointed to sit on 3 numbered chairs!!!!
Report

07/29/22

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.