Choose President & 2-Person Committee from 8 People - 168 Ways

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SUMMARY

The problem of selecting a president and a 2-person committee from a group of 8 people results in 168 distinct combinations. The calculation involves using the combination formula, specifically 8C1 for the president and 7C2 for the committee, leading to the equation 8 * 21 = 168. An alternative approach is to calculate 8C3 and multiply by 3, which also yields 168. Both methods confirm the accuracy of the solution.

PREREQUISITES
  • Understanding of combinatorial mathematics
  • Familiarity with the combination formula (nCr)
  • Basic factorial calculations
  • Knowledge of permutations versus combinations
NEXT STEPS
  • Study advanced combinatorial techniques in discrete mathematics
  • Explore applications of combinations in probability theory
  • Learn about permutations and their differences from combinations
  • Investigate real-world scenarios where committee selection is applicable
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Students in mathematics, educators teaching combinatorial concepts, and anyone interested in solving problems related to group selection and committee formation.

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Homework Statement


In how many ways can a president and a 2-person committee be chosen from a group of 8 people (where the order in which we choose the 2 people doesn't matter)? (The president cannot be on the committee.)

Homework Equations


nCr = n!/(r!*(n-r!))

The Attempt at a Solution


8C1(for president) * 7C2(for committee)
=
8*21
=
168 ways

Did I do it right?
 
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Yes. There are also multiple ways to do this problem. You could have done {}_8 C_3 \times 3 = 168.
 

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