In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls? Choose the correct answer:
A) 80 B) 81 C) 64 D) 63 E) 82
Stage 1: Select a box for the 1st ball to go into.   There are 3 available boxes, so we can complete stage 1 in 3 ways   Stage 2: Select a box for the 2nd ball to go into.   There are 3 available boxes, so we can complete stage 2 in 3 ways   Stage 3: Select a box for the 3rd ball to go into.   There are 3 available boxes, so we can complete stage 3 in 3 ways   Stage 4: Select a box for the 4th ball to go into.   There are 3 available boxes, so we can complete stage 4 in 3 ways   81y the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus distribute all 4 balls) in (3)(3)(3)(3)(4) ways (= 81 ways)   Answer:81
<result>B</result>
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?