Ten dancers A to J go to a dance competition. The following informatio...
Understanding the given information:
- There are 10 dancers: A, B, C, D, E, F, G, H, I, and J.
- There are 3 performances: Kathak, Bharatnatyam, and Folk.
- Folk dance will have a group size between 3 and 5.
- Each dancer can only perform once and must be part of exactly one group.
- A, C, E, and F know Kathak.
- B, E, G, and H know Bharatnatyam.
- All dancers except A and B know Folk dance.
- C and D cannot dance together.
- F and I have to dance together.
Step-by-step approach to solving the problem:
Step 1: Determine the possible groups for each performance.
- Kathak: The dancers who know Kathak are A, C, E, and F. Since each performance needs a minimum of 1 dancer, the possible groups for Kathak are:
- Group 1: A
- Group 2: C
- Group 3: E
- Group 4: F
- Bharatnatyam: The dancers who know Bharatnatyam are B, E, G, and H. Since each performance needs a minimum of 1 dancer, the possible groups for Bharatnatyam are:
- Group 1: B
- Group 2: E
- Group 3: G
- Group 4: H
- Folk: All dancers except A and B know Folk dance. Since Folk dance requires a group size between 3 and 5, the possible groups for Folk dance are:
- Group 1: C, D, F, G, H
- Group 2: C, D, E, G, H
- Group 3: C, D, F, G, I
- Group 4: C, D, E, G, I
- Group 5: C, D, F, G, J
- Group 6: C, D, E, G, J
- Group 7: C, D, F, H, I
- Group 8: C, D, E, H, I
- Group 9: C, D, F, H, J
- Group 10: C, D, E, H, J
Step 2: Determine the possible combinations of dancers for the given conditions.
- C and D cannot dance together. This rule eliminates the following groups for Folk dance:
- Group 1: C, D, F, G, H
- Group 3: C, D, F, G, I
- Group 5: C, D, F, G, J
- Group 7: C, D, F, H, I
- Group 9: C, D, F, H, J
- F and I have to dance together. This rule eliminates the following groups for Folk dance:
- Group 4: C, D, E, G, I
- Group 6: C, D, E, G, J
- Group 8: C, D, E, H