Question

1. In how many ways can 5 states be selected from the top 10 states with the most murders if the order of the 5 states matters?

Answer 1

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:


`P(n, r)= (n!)/((n-r)!)`

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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:


`P(10, 5)= (10!)/((10-5)!)= (10!)/(5!)=10*9*8*7*6=30,240`


Answer: 30,240