In a class of $18$ students, there are $12$ girls and $6$ boys. A chairperson, a vice-chairper

Question

In a class of $18$ students, there are $12$ girls and $6$ boys. A chairperson, a vice-chairperson and a secretary are chosen from the $18$ students. Find the number of ways the chairperson, the vice-chairperson and the secretary can be chosen so that they are all girls,[1] there are at least one girl and at least one boy.[3] The $18$ students sit at random in a circle for a lesson. Find the probability that the chairperson, the vice-chairperson and the secretary are all separated from one another,[3] there are exactly $2$ girls sitting between each boy.[3]

Accepted Answer

(a)(i) $1320$ (a)(ii) $3456$ (b) $\dfrac{91}{136}$ (c) $\dfrac1{6188}$

2023 CJC P2 Q7

2023 CJC P2 Q7

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