Respuesta :
Given n objects, assume we want to arrange r of them in a vertical or horizontal list, such that the order is important.
This can be done in P(n, r) ways, where:
[tex]P(n, r)= \frac{n!}{(n-r)!} [/tex]
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For example, there are 5 students in a race, {A, B, C, D, E}. Consider the case when the 3 winners are A, B and C.
{A, B, C}, {A, C, B}, {B, A, C}, {B, C, A}, {C, A, B}, {C, B, A} are 6 different outcomes of the race:
the first, {A, B, C} means that A is first, B is second, C third.
the second, {A, C, B} means that A is first, C is second, B third. and so on.
the race can end in P(5, 3) many ways
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Back to our problem, there are P(10, 5) many ways to list 5 out 10 states:
[tex]P(10, 5)= \frac{10!}{(10-5)!}= \frac{10!}{5!}=10*9*8*7*6=30,240[/tex]
Answer: 30,240
This can be done in P(n, r) ways, where:
[tex]P(n, r)= \frac{n!}{(n-r)!} [/tex]
-------------------------------------------------------------------------------------------------
For example, there are 5 students in a race, {A, B, C, D, E}. Consider the case when the 3 winners are A, B and C.
{A, B, C}, {A, C, B}, {B, A, C}, {B, C, A}, {C, A, B}, {C, B, A} are 6 different outcomes of the race:
the first, {A, B, C} means that A is first, B is second, C third.
the second, {A, C, B} means that A is first, C is second, B third. and so on.
the race can end in P(5, 3) many ways
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Back to our problem, there are P(10, 5) many ways to list 5 out 10 states:
[tex]P(10, 5)= \frac{10!}{(10-5)!}= \frac{10!}{5!}=10*9*8*7*6=30,240[/tex]
Answer: 30,240
