Rochelleg210idn
Answered

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in how many ways can 9 beads be arranged in a bracelet ring? a.n=_____ b. solution final answer​

Sagot :

KAntoineDoixidn

✒️PERMUTATIONS

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

[tex] \qquad \Large \:\: \rm a) \; n = 9 [/tex]

[tex] \qquad \Large \:\: \rm b) \; 720 \: ways [/tex]

*Please read and understand my solution. Don't just rely on my direct answer*

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

Since the beads are arranged in a ring, we will be using the circular permutations.

[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm P = (n-1)!} \end{align} [/tex]

Let n be the number of beads arranged on the circular bracelet ring.

  • [tex] \rm P = (9-1)! [/tex]

  • [tex] \rm P = 8! [/tex]

  • [tex] \rm P = 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 [/tex]

  • [tex] \rm P = 40,\!320 [/tex]

Therefore, there are 40,320 ways to arrange the beads in a bracelet ring.

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(ノ^_^)ノ [tex] \large\qquad\qquad\qquad\tt 3 / 4/2022 [/tex]