Permutation and Combination - Arrangements with Objects Separated

Permutation and Combination - Arrangements with Objects Separated

\(7\) red balls, \(5\) green balls and \(2\) black balls are to be arranged in a row. Assuming all balls are identical in shape and size, in how many ways can it be arranged if

  1. the green balls are grouped together,
  2. the red balls are grouped together,
  3. there is \(1\) ball between the \(2\) black balls.,

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Answer:(i) \(360\) (ii) \(168\) (iii) \(9504\)

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