MathematicsGarlands are formed using 6 red roses and 6 yellow roses of different sizes. The number of arrangements in garland which have red roses and yellow roses come alternately is

Garlands are formed using 6 red roses and 6 yellow roses of different sizes. The number of arrangements in garland which have red roses and yellow roses come alternately is

  1. A
    5!×6!
  2. B
    6!×6!
  3. C
    5!2!×6!
  4. D
    2(6!×6!)

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    Solution:

    6 yellow roses can be arranged in a circle in (61)!=5!  ways

    6 gaps can be filled by red roses in 6!  ways

    As it is a garland,

    Number of ways =12×5!×6!=5!2×6!

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