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 : ). Created by amondinamariane2006. Math

FIND THE NUMBER OF DIFFERENT WWAYS THAT A FAMILY OF 6 CAN BE SEATED AROUND A CIR...

UK2019

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✏️PERMUTATIONS

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$\underline{\mathbb{PROBLEM:}}$

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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$\underline{\mathbb{ANSWER:}}$

$\qquad\LARGE\rm» \:\: \green{120\:ways}$

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$\underline{\mathbb{SOLUTION:}}$

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

$\rm P = (n - 1)!$

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

$\rm P = (6 - 1)!$

$\rm P = 5!$

$\rm P = 5 \cdot 4 \cdot 3 \cdot 2$

$\rm P = 120$

$\therefore$ There are 120 ways to arrange the family of 6 in a circular table with 6 chairs.

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#CarryOnLearning

MasterOfMathProblem hey sir/ma'am, what grade are you in?

UK2019 senior high na po

MasterOfMathProblem ok, I see

MasterOfMathProblem

✒️CIRCULAR

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

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 $\tt \: n$ objects can be arranged in a circle in $\tt \: (n-1)!$ ways.

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

#CarryOnLearning

$\qquad\qquad\qquad\qquad\qquad\qquad\tt{04-03-2022} \\ \qquad\qquad\qquad\qquad\qquad\qquad\tt{10:47\: am}$

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✏️PERMUTATIONS

✒️CIRCULAR

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