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  • Determine how many different ways 9 flags can be arranged on a flagpole.  Option: 1 20420<div class='qna-optio

Determine how many different ways 9 flags can be arranged on a flagpole.

 

Option: 1

20420


Option: 2

43520


Option: 3

51320


Option: 4

40320


Answers (1)

best_answer

To determine the number of different ways 9 flags can be arranged on a flagpole, we can use the concept of circular permutations.

Since the flagpole forms a closed loop, the arrangement of the flags is considered a circular permutation. In a circular permutation, the relative order of the objects matters, but the starting point does not.

The number of circular permutations of a set of objects is given by \begin{aligned} (n-1) ! \end{aligned} , where n is the number of objects.

In this case, there are 9 flags, so the number of circular permutations is:

\begin{aligned} &(9-1) !=9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2\\ &(9-1) !=40320 \end{aligned}

Hence, there are 40,320 different ways to arrange the 9 flags on the flagpole.

Posted by

Ritika Kankaria

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