There are 6 people in a group that walk into a restaurant. The only table open is a 4-person table. In how many different ways can 4 people be seated at the table if we don't care where the 4 people sit at the table?

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Answer 1 · 2017-02-12T15:20:43

15

This is a combinations problem, in that seating persons A, B, C, D is the same as seating D, C, B, A.

We can solve this using the combinations general formula:

#C_(n,k)=(n!)/((k)!(n-k)!)# with #n="population", k="picks"#

Substituting in #n=6, k=4#:

#(6!)/((4)!(6-4)!)=(6!)/((4!)(2!))=(6xx5xx4!)/(4!xx2)=30/2=15#