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in how many ways can five keys be arranged in a keyring​

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AGBOIIIN

[tex] \large\underline \mathcal{{QUESTION:}}[/tex]

in how many ways can five keys be arranged in a keyring?

[tex]\\[/tex]

[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]

» Keyring is a circular manner permutation , thus we will use the circular permutation.

  • [tex]\sf{P_{circular}=(n-1)!}[/tex]

[tex]\\[/tex]

Given that n = 5

[tex]\sf{P_{circular}=(n-1)!}[/tex]

[tex]\sf{P_{circular}=(5-1)!}[/tex]

[tex]\sf{P_{circular}=4!}[/tex]

[tex]\sf{P_{circular}=4\times3\times2\times1}[/tex]

[tex]\sf{P_{circular}=24}[/tex]

[tex]\\[/tex]

[tex] \large\underline \mathcal{{ANSWER:}}[/tex]

  • There are 24 ways

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