How many ways can 6 different sea shells be displayed on a s

Solution

Permutations consider the order of items in a group, and count each different order as a different option. A permutation is a unique arrangement of items. The number of permutations on a set of n elements is given by n!

It is presumed that the top of the bucket is circular. Since the sea shells are being put up for display, it is also presumed that these are being arranged in a circle. Now, if we arrange 6 objects in a circle, 5 objects only have to be arranged. The arrangement of the 6^th object, then, does not leave any choices. Therefore, the number of ways in which 6 sea shells can be arranged in a bucket on a shelf is 5! = 5 *4*3*2*1 = 120.

NOTE: If the sea shells were to be arranged in a line, then the answer would have been 6!.