2021 SJI P1 Q5

2021 SJI P1 Q5

IB Year 5 | Grade 11
8 marks

For this question, leave all answers in factorial form, in terms of \(m\) and/or \(n\).

\(m\) boys and \(n\) girls are to be seated in a row, where \(m\) and \(n\) are positive.

Find the number of ways this can be done in each of the following cases:

  1. there are no restrictions;[1]
  2. the \(n\) girls are seated together;[2]
  3. a particular boy and a particular girl must be adjacent;[2]
  4. no boys are adjacent given that there are equal numbers of boys and girls. Leave your answer in terms of \(n\).[3]

Solution:

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Answer:(a) \((m+n)!\) (b) \(n!(m+1)!\) (c) \(2!(m+n-1)!\) (d) \(n!(n+1)!\)

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