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6 women and 8 men attended a dating event. Julie and Kayla are among the female participants while Bernard and Charlie are among the male

6 women and 8 men attended a dating event. Julie and Kayla are among the female participants while Bernard and Charlie are among the male participants.

(i) How many ways can all the participants stand in a circle such that no two women stand next to each other?

The participants are divided into two groups of 3 women each and two groups of 4 men each to play a game.

(ii) How many ways can this be done if there is no restriction?

(iii) How many ways can this be done if Julie and Kayla are in the same group while Bernard and Charlie are in different groups?

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