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Find the number of ways in which 12 diff...

Find the number of ways in which 12 different beads can be arranged to form a necklace.

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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. So the required number of arrangements=`(1)/(2)(11!)`.
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ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
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  2. There is a rectangular sheet of dimension (2m-1)xx(2n-1), (where m > 0...

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  3. If the letters of the word SACHIN are arranged in all possible ways ...

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  4. lf r, s, t are prime numbers and p, q are the positive integers such t...

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  5. At an election, a voter may vote for any number of candidates not grea...

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  6. The letters of the word COCHIN are permuted and all the permutation...

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  7. The set S""=""{1,""2,""3,""........ ,""12) is to be partitioned into...

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  8. Consider all possible permutations of the letters of the word ENDEANOE...

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  9. The number of words can be formed with the letters of the word 'MATHEM...

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  10. In a shop, there are five types of ice-creams available. A child buys ...

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  11. The number of seven digit integers, with sum of the digits equal to 10...

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  12. Three boys and two girls stand in a queue. The probability that the nu...

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  13. There are two urns. Urn A has 3 distinct red balls and urn B has 9 ...

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  14. In how many ways 5 different balls can be distributed into 3 boxes so ...

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  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

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  16. The total number of ways in which 5 balls of differert colours can be ...

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  17. Let n denote the number of all n-digit positive integers formed by the...

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  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  19. Assuming the balls to be identical except for difference in colours, t...

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  20. Let Tn be the number of all possible triangles formed by joining ve...

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  21. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

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