### Permutation; debate team

Question Sample Titled 'Permutation; debate team'

There are ${20}$ students in Class ${6}{B}$ . ${4}$ of them are chosen to be the first speaker, the second speaker, the third speaker and the last speaker of a debate team.

 (a) (i) How many permutations are there to form the debate team？ (ii) If Karen and Gabriel are already chosen to be the team members, find the probability that they speak next to each other.  (2 marks) (b) After the debate team members were chosen, another ${3}$ students are chosen to ask questions in the last session. It is given that Stephanie is not a debate team member. Find the probability that she is not chosen to ask questions in the last session. (2 marks)

 (ai) Number of permutations for forming the debate team  $={{P}_{{4}}^{{20}}}$  $={116280}$ 1A (aii) The required probability  $=\dfrac{{{2}!\times{3}!}}{{{4}!}}$  $=\dfrac{{1}}{{2}}$ 1A  (b) Number of students who are not debate team members  $={20}-{4}$  $={16}$ The required probability  $=\dfrac{{15}}{{16}}\times\dfrac{{14}}{{15}}\times\dfrac{{13}}{{14}}$ 1M  $=\dfrac{{13}}{{16}}$ 1A

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