I WILL CHOOSE BRAINIEST AND 5 STARS AND A THANKS... 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?

When looking at this problem, there are 13 beads that can be put on first, 12 that can be put on second as the first one was already used, 11 put on third, and so on. This means the amount of necklaces you can make are 13*12*11...*2*1, or 13 factorial (13!). But since you can rotate the necklace this means that there are each combination has 12 others just like it, just rotated(13 in total). This means we must divide 13! by 13, which makes it 12!. 12! is equal to 479,001,600, which is the answer.

HumanBein HumanBein · Answer 2 · 2020-07-12T17:42:09+02:00

Answer:

6,227,020,800 different necklaces.

Step-by-step explanation:

To start making the necklace, you will have to choose one of the 13 beads. For the next bead, you will have 13 - 1 = 12 beads to choose from. For the next bead, you will have 12 - 1 = 11 beads to choose from, and so on and so forth, until all 13 beads are used.

So, you will have 13! different necklaces, since you would have 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 156 * 110 * 72 * 42 * 120 = 17160 * 362880 = 6227020800.

So, you will have 6,227,020,800 different necklaces.

Hope this helps!