Question

probability question!
a)
three balls are placed at random in three boxes, with no restriction on the number of balls per box; list the 27 possible outcomes of this experiment. find the probability of each of the following events:
A: the first box is empty
B: the first two boxes are empty
C: no box contains more than one ball
b) find the probabilities of events A, B and C when three balls are placed at random in n boxes(n>=3)
c) find the probabilities of events A, B and C when r balls are placed in n boxes(n>=r)

Answer 1

for part a), I got 8/27, 1/27,2/9
however i am having trouble with part b and c

Answer 2

how to generalize a formula for part b and c?

Answer 3

is your first answer correct

Answer 4

yes. i am 100% sure

Answer 5

A) may be 1/3

Answer 6

? how come...? because i have already listed all the possible outcome and turns out to be 8/27

Answer 7

ok ok you r correct it is 2^3 not3^2 i misstook

Answer 8

what bothers me the most is part b) and part c). I have no idea how to find a formula for b) and c)

Answer 9

then i will explain part b and c

Answer 10

ok. thank you :D

Answer 11

for b
see we have three balls and n boxes that is n choises for each ball so the total ways of arranging 3 in n is n^3
now in case b we lost a box so we have n-1 choises for each box it is (n-1)^3 ways
hence probability is