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Amondinamariane2006go
Answered

FIND THE NUMBER OF DIFFERENT WWAYS THAT A FAMILY OF 6 CAN BE SEATED AROUND A CIRCULAR TABLE WITH 6 CHAIR .

PLEASE SHOW THE SOLUTION : )

Sagot :

UK2019go

✏️PERMUTATIONS

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[tex]\underline{\mathbb{PROBLEM:}}[/tex]

  • Find the number of different ways that a family of 6 can be seated around a circular table with 6 chairs.

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[tex]\underline{\mathbb{ANSWER:}}[/tex]

[tex]\qquad\LARGE\rm» \:\: \green{120\:ways}[/tex]

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[tex]\underline{\mathbb{SOLUTION:}}[/tex]

- Apply the Circular Permutation to identify the number of ways if n objects are arranged in a circle.

  • [tex] \rm P = (n - 1)![/tex]

- Let n be the family of 6 arranged in a circular table with 6 chairs.

  • [tex] \rm P = (6 - 1)![/tex]

  • [tex] \rm P = 5![/tex]

  • [tex] \rm P = 5 \cdot 4 \cdot 3 \cdot 2[/tex]

  • [tex] \rm P = 120[/tex]

[tex]\therefore[/tex] There are 120 ways to arrange the family of 6 in a circular table with 6 chairs.

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MasterOfMathProblemgo

✒️CIRCULAR

[tex] \tt \: Using \: the \: formula \\ \tt \\ \tt \implies P = (n-1)! \\ \tt \implies thus \: P = (6 - 1) \\ \tt \implies P =5 ! \\ \tt \implies P= 5 \times 4 \times 3 \times 2 \times 1 \\ \tt \:\tt \implies P\red{= 120 \: ways } \ \: [/tex]

This is an example of a circular permutation, in which we are asked to find the number of ways to arrange a distinct number of elements in a circular manner and thus, order matters.

The circular permutation formula states that the number of [tex]\tt \: n[/tex] objects can be arranged in a circle in [tex]\tt \: (n-1)![/tex] ways.

Hence, to answer this problem, there are [tex]\tt \:(6-1)![/tex] ways to arrange a family of 6 around a circular table with 6 chairs.

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[tex]\qquad\qquad\qquad\qquad\qquad\qquad\tt{04-03-2022} \\ \qquad\qquad\qquad\qquad\qquad\qquad\tt{10:47\: am}[/tex]

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