Multiple choice

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.

In how many ways can a team consisting of exactly three boys be formed?

  1. 4

  2. 5

  3. 6

  4. 7
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B Correct answer
AI explanation

We need to select exactly 3 boys from the 4 available boys, which can be done in 4C3 = 4 ways. We then need to select 2 girls to complete the 5-member team, but the specific combinations of boys chosen invoke restrictions on which girls can be selected. Evaluating the valid combinations based on the conditional rules for each boy yields 5 distinct valid teams.

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