Our club has $25$ members, and wishes to pick a president, secretary, and treasurer. In how many ways can we choose the officers, if individual members are allowed to hold $2,$ but not all $3,$ offices?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Our club has $25$ members, and wishes to pick a president, secretary, and treasurer. In how many ways can we choose the officers, if individual members are allowed to hold $2,$ but not all $3,$ offices?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
15,600
Our club has $25$ members, and wishes to pick a president, secretary, and treasurer. In how many ways can we choose the officers, if individual members are allowed to hold $2,$ but not all $3,$ offices?
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