The Winner’s Club consists of $2$ married couples and $8$ singles. The club is to select a deleg

Question

The Winner’s Club consists of $2$ married couples and $8$ singles. The club is to select a delegation of $4$ members to participate in an overseas conference. Find the probability that the delegation contains exactly one married couple. [2] The $4$ selected delegates from the Winner’s Club are invited for a photo shoot with $8$ delegates from other clubs after the conference. They are required to stand in two rows of $6$. Find the probability that at least $3$ delegates from the Winner’s Club stand in the same row.[3] TGM probability model: all four-member delegations are equally likely. For the photograph, all arrangements of the twelve distinct delegates in the twelve positions are equally likely.

Accepted Answer

(i) $\dfrac8{45}$ (ii) $\dfrac6{11}$

2013 AJC P2 Q6

2013 AJC P2 Q6

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