How Many Ways Can an 8 Oar Boat Crew Be Selected from 11 People?

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SUMMARY

The problem involves selecting a crew of 8 for an oar boat from a pool of 11 individuals, categorized by their rowing capabilities. Specifically, 5 individuals can row only on one side, 4 can row only on the opposite side, and 2 are versatile rowers capable of rowing on either side. The solution requires calculating the combinations based on different configurations of rowers, ensuring an equal distribution of strength on both sides to maintain balance. The analysis leads to determining the total number of valid crew configurations that adhere to these constraints.

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  • Understanding of combinatorial mathematics
  • Familiarity with basic principles of probability
  • Knowledge of constraints in selection problems
  • Ability to apply the concept of combinations and permutations
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  • Learn about constraints in combinatorial problems
  • Explore advanced topics in probability theory
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Students studying combinatorics, educators teaching probability and selection methods, and anyone interested in solving mathematical problems related to team selection and resource allocation.

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Homework Statement


A crew of an 8 oar boat has to be selected from 11 people, out of which 5 can oar only on one side, 4 can oar only on the other side and 2 can oar on either sides, find in how many ways can the selection be done?



The Attempt at a Solution



What I did here is assumed 3 possibilities
1. 7 on one side and 4 on the other---- assuming those two to be on one side
2. 6 on one side and 5 on the other---- equally dividing them on each side
3. 5 on one side and 6 on the other---- equally dividing them on each side
 
Physics news on Phys.org
In Oaring a boat, you have to man equal strength on either side or the boat will no go straight. Here, select 4 people for right side and 4 people for left side.
 

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