A school Grad Committee of three students is to be formed from 7 male and 5 female grade 12 students

Question

a. Determine the total number of ways the committee may be formed.

b.Determine the total number of ways the committee may be formed If the three committee members fill distinct roles for Chair, Treasurer and Event Coordinator.

c. Explain the difference between a permutation and combination using the different scenarios described for part a and part c.

d. Determine the total number of ways the committee from part a may be formed if there must be at least one male student on the committee.

Answer 1

a) C(12,3) = 12!/(9!·3!) = 220

b) P(12,3) = 12!/9! = 1320

c) 2 combination differ only by elements, but permutations differ or by elements or by order or by both

d) C(12,3) - C(5,3) = 220 - 10 = 210