A group of $12$ people consist of $5$ men and $7$ women. One of the women is the wife of one o

Question

A group of $12$ people consist of $5$ men and $7$ women. One of the women is the wife of one of the men. How many committees of $5$ can be formed which include at least $3$ women?[2] The $12$ people sit at random at a round table. Find the probability that the husband and his wife are seated together and no two men are next to each other.[3]

Accepted Answer

(a) ${546}$ (b) ${\frac{1}{77}}$

2022 YIJC P2 Q6

2022 YIJC P2 Q6

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