You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
There are three video game systems: the Paystation, the WHAT, and the ZBoz2\(\pi\), and none of these systems will play games for the other systems. Uncle Riemann has three nephews: Bernoulli, Galois, and Dirac. Bernoulli owns a Paystation and a WHAT, Galois owns a WHAT and a ZBoz2\(\pi\), and Dirac owns a ZBoz2\(\pi\) and a Paystation. A store sells \(4\) different games for the Paystation, \(6\) different games for the WHAT, and \(10\) different games for the ZBoz2\(\pi\). Uncle Riemann does not understand the difference between the systems, so he walks into the store and buys \(3\) random games (not necessarily distinct) and randomly hands them to his nephews. What is the probability that each nephew receives a game he can play? The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\).
user
32
rule
There are three video game systems: the Paystation, the WHAT, and the ZBoz2\(\pi\), and none of these systems will play games for the other systems. Uncle Riemann has three nephews: Bernoulli, Galois, and Dirac. Bernoulli owns a Paystation and a WHAT, Galois owns a WHAT and a ZBoz2\(\pi\), and Dirac owns a ZBoz2\(\pi\) and a Paystation. A store sells \(4\) different games for the Paystation, \(6\) different games for the WHAT, and \(10\) different games for the ZBoz2\(\pi\). Uncle Riemann does not understand the difference between the systems, so he walks into the store and buys \(3\) random games (not necessarily distinct) and randomly hands them to his nephews. What is the probability that each nephew receives a game he can play? The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\).
train