In how many ways can 3 students from a class of 16 be chosen for a field trip?

Question

In how many ways can 3 students from a class of 16 be chosen for a field trip?

Answer 1

Is the order relevant?

 

For example, is Mike, Joe, and Steve considered

to be the same selection as Steve, Mike, and Joe?

 

If order is relevant, then there are 16*15*14 = 3360

 

If order does not matter, then there is

(16 choose 3) = 16!/(3!*13!) = 16*15*14/(3*2*1)

                                            = 8*5*14   <---     16 cancels the 2;  15 cancels the 3

 

                                            = 560