# How many outcomes are in this situation

i just want to check if my answer is correct.

10 distinct balls are to be tossed, one at a time, intto 5 distinct bins. find the number of possible outcomes the following case.

a) an outcome records only the identity of the bin for each toss (no record of the ball tossed)

b) an outcome records the identity of each ball and its bin (no record of the order in which balls are tossed)

wouldn't the answer be 5^10? since each ball has 10 possible bins that it can be tossed into and there are 5 balls so 5^10?

for b would it be the same answer as a?

thanks

## Answers and Replies

chiro
Science Advisor
i just want to check if my answer is correct.

10 distinct balls are to be tossed, one at a time, intto 5 distinct bins. find the number of possible outcomes the following case.

a) an outcome records only the identity of the bin for each toss (no record of the ball tossed)

b) an outcome records the identity of each ball and its bin (no record of the order in which balls are tossed)

wouldn't the answer be 5^10? since each ball has 10 possible bins that it can be tossed into and there are 5 balls so 5^10?

for b would it be the same answer as a?

thanks

You're correct.

An easy way to reason for this problem is to consider that:

a) Every ball is independent from the others
b) There are five choices per ball. (ie P(A) = 1/5)

Because of the independence P(A and B) = P(A)P(B)

If you didn't have independence then it would not work out this way.

Also you said there are 10 possible bins when there are only five. For each ball you only have 5 bins and a 1/5 probability for each ball to land in any bin for each bin assuming equally likely probability.

i just want to check if my answer is correct.

10 distinct balls are to be tossed, one at a time, intto 5 distinct bins. find the number of possible outcomes the following case.

a) an outcome records only the identity of the bin for each toss (no record of the ball tossed)

b) an outcome records the identity of each ball and its bin (no record of the order in which balls are tossed)

wouldn't the answer be 5^10? since each ball has 10 possible bins that it can be tossed into and there are 5 balls so 5^10?

for b would it be the same answer as a?

thanks

Hi Kevinf,

It's a matter of interpretation of the problem statement, but I agree with you on b) but not a). It seems to me that a) is asking for the number of sequences of 10 choices where you have 2 possibilities for each choice. For example, if the bins are A and B, a possible sequence would be ABBABBBAA.