Question 88734

*[Tex \LARGE \textrm{_{n}P_{r}=\frac{n!}{(n-r)!}}] Start with the given formula


*[Tex \LARGE \textrm{_{12}P_{4}=\frac{12!}{(12-4)!}}] Plug in {{{n=12}}} and {{{r=4}}}


*[Tex \LARGE \textrm{_{12}P_{4}=\frac{12!}{8!}}] Subtract {{{12-4}}} to get 8


*[Tex \LARGE \textrm{_{12}P_{4}=\frac{479001600}{8!}}] Calculate 12! to get 479,001,600 (note: if you need help with factorials, check out this <a href=http://www.algebra.com/algebra/homework/Probability-and-statistics/factorial.solver>solver</a>)


*[Tex \LARGE \textrm{_{12}P_{4}=\frac{479001600}{40320}}] Calculate 8! to get 40,320


*[Tex \LARGE \textrm{_{12}P_{4}=11880] Divide 479,001,600 by 40,320 to get 11,880



So 12 choose 4 (where order does matter) yields 11,880 unique combinations