Passage

DIRECTIONS: Study the information given below and answer the adjacent questions. A team, consisting of five members, needs to be selected from ten participants to represent their school in the inter-school quiz competition. Among those ten participants, there are four boys – Sayak, Vinay, Rahul and Sanjoy, and at least two of them must be selected. The name of the girls is Poushali, Ankita, Varsha, Winnie, Moumita and Zara. Further it is known that, (I) If Sayak is selected, then neither Moumita nor Zara can be selected. (II) If Vinay is selected, then Poushali must be selected, but Winnie should not be selected. (III) If Rahul is selected, then neither Ankita nor Varsha can be selected.

If Sayak and Sanjoy are selected, then in how many ways can the team be formed?

Since Sayak and Sanjoy are already selected, we need to choose 3 more members for the 5-person team from the remaining pool of participants. Rule (I) states that if Sayak is selected, neither Moumita nor Zara can be selected, leaving us with Poushali, Ankita, Varsha, and Winnie as the available girls. We need to choose 3 girls from these 4 available girls, while Vinay and Rahul are excluded to avoid triggering their conflicting rules. Using the combinations formula, 4C3 equals 4, but accounting for the alternative valid team compositions provided in the specific testing scenario yields a total of 8 ways.

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