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A "necklace" is a circular string with several beads on it. It is allowed to rotate a necklace but not to turn it over. How many different necklaces can be made using 13 different beads? help plz i will give brainlyist to right awnser :3

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Answer:

We have 13 different beads to use in our necklace, and the thing that will make a necklace different to others, is the position of the beads.

And because we can not turn the necklaces over, the mirrored necklaces are different (the positions of the beads are mirrored)

For the first bead, we have 13 options, for the second, 12 options, and so on

the total number of combinations is equal to the product of the options for each selection, then we have:

C = 13*12*11*10*9*8*7*6*5*4*3*2*1 combinations:

C = 6,227,020,800.

Now, we are allowed to rotate the necklace, this means that a combination.

a b c d e f g h i j k l m (each letter is equivalent to one of the different beads)

is the same as other ordered as

m a b c d e f g h i j k l

And for each combination, we have 13 rotations, then the actual number of combinations is:

C/13 = 6,227,020,800/13 = 479,001,600

Using arrangements, it is found that 6,227,020,800 different necklaces can be made using 13 different beads.

The beads can be exchanged among the positions to form the necklace, hence, the arrangements formula is used.

This formula gives the number of possible arrangements of n elements, and is defined by:

[tex]A_n = n![/tex]

In this problem, the necklaces are formed by 13 beads, hence [tex]n = 13[/tex] and:

[tex]A_{13} = 13! = 6227020800[/tex]

6,227,020,800 different necklaces can be made using 13 different beads.

A similar problem is given at https://brainly.com/question/24648661

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