If there are atleast three women in the team, then which of the following is a correct selection of the team?
The objective is to identify the correct team selection of 5 members from 5 men and 6 women, adhering to specific constraints and a condition regarding the number of women.
Team Selection Conditions & Constraints
- Team Size: Exactly 5 members.
- Minimum Women: At least 3 women must be in the team.
- M2/M5 Pairing: M2 and M5 must be selected together or not at all.
- M1/M3 Exclusion: M1 and M3 cannot be selected together.
- M5 Exclusion Rule: If M5 is selected, W4 and M4 cannot be selected.
- W6 Exclusion Rule: If W6 is selected, M2, W1, and W2 cannot be selected.
- W5 Exclusion Rule: If W5 is selected, W6, W2, and M2 cannot be selected.
Analysis of Team Selection Options
Option 1: {M2, W2, W4, M5, W6}
- Women Count: 3 (W2, W4, W6) - Meets the minimum requirement.
- M2/M5 Pairing: M2 and M5 are present. - OK.
- Constraint Violation: W6 is selected, but M2 is also selected. This violates the rule "W6 cannot be selected with M2".
- Constraint Violation: M5 is selected, but W4 is also selected. This violates the rule "M5 cannot be selected with W4".
This option is incorrect due to multiple constraint violations.
Option 2: {M2, W3, M5, M3, W2}
- Women Count: 2 (W3, W2) - Does NOT meet the minimum requirement of 3 women.
This option is incorrect as it fails the primary condition.
Option 3: {M1, W5, W4, M4, W3}
- Women Count: 3 (W5, W4, W3) - Meets the minimum requirement.
- M2/M5 Pairing: Neither M2 nor M5 is selected. - OK.
- M1/M3 Exclusion: M1 is selected, M3 is not selected. - OK.
- M5 Exclusion Rule: M5 is not selected. - OK.
- W6 Exclusion Rule: W6 is not selected. - OK.
- W5 Exclusion Rule: W5 is selected. The excluded members (W6, W2, M2) are not selected. - OK.
This option satisfies all conditions and constraints.
Option 4: {M1, W2, W4, W6, M3}
- Women Count: 3 (W2, W4, W6) - Meets the minimum requirement.
- M1/M3 Exclusion: M1 and M3 are both selected. - VIOLATES the rule "M1 cannot be selected with M3".
This option is incorrect due to violating the M1/M3 exclusion rule.
Conclusion
Based on the analysis, only Option 3 meets all the specified requirements for team selection.
Similar Questions
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