In how many ways can a committee of 3 men and 2 women be chosen such that one specific man and one specific woman are invariably included?
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Answer: C. 30
Explanation
Involving one specific man and one specific woman permanently reduces the remaining selection pool requirements. Selecting two additional men from the remaining available pool requires evaluating binomial coefficient combinations. Choosing one additional woman from the remaining female pool and multiplying combinations yields thirty total ways. Combinations calculate the number of ways to choose items from a larger set without regard to selection order. Mandatory inclusion rules simplify committee selection problems by pre-allocating specific positions to designated individuals. Multiplying independent choice combinations together determines the total number of valid committee formation structures.
Organizations form specialized subcommittees by mandating key leadership presence while electing remaining members democratically. Human resource recruiters assemble interview panels by ensuring specific department heads are always included in groups. Tournament organizers select referee committees by guaranteeing representation from designated regional administrative branches. Option A suggests one hundred ways which significantly overestimates the combinatorial possibilities for these pool sizes. Option B proposes sixty ways which doubles the correct mathematical product of the remaining group combinations. Option D implies twenty ways which underestimates the number of ways to choose the remaining members.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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