The number of combinations nine objects taken six at a time
The number of combinations of selecting six objects from a set of nine objects can be calculated using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
where n is the total number of objects and r is the number of objects being selected.
In this case, n = 9 and r = 6.
C(9, 6) = 9! / (6! * (9-6)!)
= 9! / (6! * 3!)
= (9 * 8 * 7 * 6!) / (6! * 3 * 2 * 1)
= (9 * 8 * 7) / (3 * 2 * 1)
= 84
Therefore, there are 84 combinations of selecting six objects from a set of nine objects.