A technology startup needs to form a 4-member project team selected from a pool of 5 front-end developers and 5 back-end developers. However, the selection is subject to one condition: if a specific front-end developer, Elena, is selected for the team, then a specific back-end developer, Marcus, must also be selected for the team. How many different 4-member teams can be formed under this condition?
Cevap: 154 teams
Cevap
154 different 4-member teams can be formed under the given condition.
The total number of ways to select a 4-member team from 10 developers without restrictions is . The conditional restriction requires that whenever Elena is on the team, Marcus must also be on the team. The only selection that violates this rule is one where Elena is included but Marcus is excluded. For this invalid scenario, Elena takes 1 spot and Marcus is removed from consideration, leaving ways to pick the remaining 3 members from the remaining 8 developers. Subtracting these 56 invalid teams from the 210 total teams gives 154 valid teams.
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Anahtar Kavram
Combinations with Conditional Restrictions (Complementary Counting)
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