Permutations And Combinations Question 351

Question: Number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour.

Options:

A) $ 6\times {{(9!)}^{2}} $

B) 12!

C) $ 4\times {{(8!)}^{2}} $

D) $ 5\times {{(9!)}^{2}} $

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Answer:

Correct Answer: D

Solution:

  • [d] Ten pearls of one colour can be arranged in $ \frac{1}{2}.(10-1)! $ ways. The number of arrangements of 10 pearls of the other colour in 10 places between the pearls of the first colour =10!
    $ \therefore $ Required number of ways $ =\frac{1}{2}\times 9!\times 10!=5{{(9!)}^{2}} $