**Contents**show

## How many ways 8 different beads can be arranged to form a necklace?

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

## How many ways can 7 beads be strung into necklace?

2520. **5040**.

## 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 5 beads are used to make a necklace?

One is clockwise, another is anticlockwise. Here in both directions we will get the same arrangement. So, we have to divide 24 by 2. Therefore the total number of different ways of arranging 5 beads is 242=**12** .

## How many different ways can the 8 persons be seated in a circular table?

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

## How many ways can 6 beads be arranged in a string?

6P6 = **720** or 6!

## 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.

## How many ways can the 7 persons be seated in a circular table?

Since in this question we have to arrange persons in a circle and 7 persons have to be arranged in a circle so that every person shall not have the same neighbor. Hence there are **360 ways** to do the above arrangement and therefore the correct option is A. So, the correct answer is “Option A”.

## How many ways 10 beads can be arranged?

Answer: 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 5 people arrange themselves in a line?

Answer: If the symmetry of the table is not taken into account the number of possibilities is 5! = **120**. In this case it would be the same as ordering people on a line. However if rotation symmetry is taken into account, there are five ways for people to sit at the table which are just rotations of each other.

## How many necklace of 12 beads each can be made from 18 beads of different Colours?

Correct Option: C

First, we can select 12 beads out of 18 beads in ^{18}C_{12} ways. Now, these 12 beads can make a necklace in **11! / 2 ways** as clockwise and anti-clockwise arrangements are same. So, required number of ways = [ ^{18}C_{12} . 11! ] / 2!