Four girls (G1, G2, G3, G4) and three boys (B1, B2, B3) are to sit for a dinner such that no two boys should sit together nor two girls. If they are successively sitting, what is the position of B2 and G3?
- 5th and 6th
- 4th and 5th
- 3rd and 4th
- 2nd and 3rd
The Correct Option is B
Solution and Explanation
There are 4 girls (G1, G2, G3, G4) and 3 boys (b1, b2, b3).
No two boys or two girls can sit together, meaning the seating must alternate between boys and girls.
The seating is successive, implying that every seat alternates between a boy and a girl.
Since there are 4 girls and 3 boys, the seating arrangement must start and end with a girl (because there are more girls than boys).
\(G, b, G, b, G, b, G\)
b2 can sit in one of the three positions assigned for boys: the 2nd, 4th, or 6th position.
G3 can sit in one of the four positions assigned for girls: the 1st, 3rd, 5th, or 7th position.
Seating arrangement starts from G1, and follows the order G1, b1, G2, b2, G3, b3, G4:
b2 is in the 4th position.
G3 is in the 5th position.
Therefore, the position of b2 is 4th, and the position of G3 is 5th.
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