They are 15 entrees available at a restaurant. from these, archie is to choose 6 for his party. how many groups of 6 entrees can he choose assuming the order entry does not matter

In this item, we are informed that the order of the entries does not matter in determination the number of ways in which the Archie can choose for his party. Because the arrangement or order is not important, this type of problem uses the concept of COMBINATION.

The equation for combination is,
     nCr = n!/((n - r)!(r!))

nCr is read as "combination of n taken r".

Substituting the known values to the equation,
   15C6 = 15! / ((15 - 6)!(6!))
             = 5005

Hence, there are 5005 ways in which Archee can choose the 6 entrees for his party.