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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in how many ways can a president, vice president, and a secretary be chosen?... is it 12X11X10. Permutation of n things taken r at a time: nPr=n!/(n-r)! 12P3=12*11*10*9!/9!= 12*11*10=1320 ways.
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1320
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