**Contents**show

## How many ways can nine beads be placed on a bracelet with no clasp?

This is called a cyclic permutation. The formula for this is simply (n-1)!/2, since all the beads are identical. Hence, the answer is 9!/2 = 362880/2 = **181440**.

## How many ways can 8 persons be seated at a round table?

ways, where n refers to the number of elements to be arranged. = **5040 ways**.

## How many ways can letters be arranged?

Now, the formula of expanding factorial is n! =n×(n−1)×(n−2)×…… ×3×2×1. Therefore, we can arrange the letters in the word ‘FACTOR’ in **720 ways**.

## How many ways can 7 beads can be arranged to form a necklace?

2520. **5040**.

## How many ways can 3 people sit in a round table?

So there are two answers: There are 3! = **6 different ways** of placing these three people in three distinct chairs. However, it we decide to consider rotated arrangements as basically the same, then there are only 2 ways.

## How many necklaces can you make with 6 beads of 3 colors?

The first step is easy: the number of ways to colour 6 beads, where each bead can be red, green or blue, is 3^{6} = **729**. Next we put the beads on a necklace, and account for duplicate patterns.

## How many ways can you arrange things in a circle?

Coming back to the question – In how many ways can 5 distinct objects be arranged in a circle? Now there are 5! or **120 different linear arrangements possible**.

## How many ways can 12 beads be arranged on a bracket?

12 different beads can be arranged among themselves in a circular order in **(12-1)!=** **11!** **Ways**. Now, in the case of necklace, there is not distinction between clockwise and anti-clockwise arrangements.

## How many ways can eight beads no two of which are the same be arranged on a chain with a clasp?

**2520 Ways** 8 beads of different colours be strung as a necklace if can be wear from both side.

## How many bracelets can be made by stringing 9 different colored beads together?

by stringing together 9 different coloured beads one can make **9!** **(9 factorial )** bracelet. 9! = 9×8×7×6×5×4×3×2×1 = 362880 ways.