Solution Found!
Suppose that n indistinguishable balls are to be arranged
Chapter 2, Problem 181SE(choose chapter or problem)
Suppose that n indistinguishable balls are to be arranged in N distinguishable boxes so that
each distinguishable arrangement is equally likely. If \(n \geq N\), show that the probability no box will be empty is given by
\(\frac{\left(\begin{array}{c}
n-1 \\
N-1
\end{array}\right)}{\left(\begin{array}{c}
N+n-1 \\
N-1
\end{array}\right)}
\)
Equation Transcription:
Text Transcription:
n >/= N
(n-1 N-1) over (N+n-1 N-1)
Questions & Answers
QUESTION:
Suppose that n indistinguishable balls are to be arranged in N distinguishable boxes so that
each distinguishable arrangement is equally likely. If \(n \geq N\), show that the probability no box will be empty is given by
\(\frac{\left(\begin{array}{c}
n-1 \\
N-1
\end{array}\right)}{\left(\begin{array}{c}
N+n-1 \\
N-1
\end{array}\right)}
\)
Equation Transcription:
Text Transcription:
n >/= N
(n-1 N-1) over (N+n-1 N-1)
ANSWER:
Solution:
Step 1 of 2:
Here n indistinguishable balls are to be arranged in N distinguishable boxes. Each distinguishable arrangement is equally likely.
If n, we have to show that the probability that no box will be empty is