What's 10P5? What's 9C3?

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Answer 1 · 2017-02-26T12:11:43

#P_(10,5)=30,240; C_(9,3)=84#

#P_(10,5)#

This is the permutation of a population of 10, choosing 5. The general formula for a permutation is:

#P_(n,k)=(n!)/((n-k)!); n="population", k="picks"#

#P_(10,5)=(10!)/((10-5)!)=(10!)/(5!)=>#

#10xx9xx8xx7xx6=30,240#

#C_(9,3)#

This is the combination of a population of 9, choosing 3. The general formula for a combination is:

#C_(n,k)=(n!)/((k)!(n-k)!)# with #n="population", k="picks"#

#C_(9,3)=(9!)/((3)!(9-3)!)=(9!)/((3!)(6!))=>#

#(cancel9^3xxcancel8^4xx7xxcancel(6!))/(cancel3xxcancel2xxcancel(6!))=3xx4xx7=84#