Given there are k5 balls that we need to put into 3 buckets

Given there are k=5 balls that we need to put into 3 buckets. How many different results are there if the buckets all have different labels but the balls have no labels?

Solution

IN THE FIRST BUCKET WE CAN CHOOSE 1 BALL OF 5 BALLS

IN THE SECOND BUCKET WE CAN CHOOSE 1 BALL OF 4 BALLS

IN THE 3 BUCKET WE CAN CHOOSE 1 BALL OF 3 BALLS

DIFFERENT WAYS = 5*4*3 =60

60 DIFFERENT WAYS