Answer to Question #256432 in Discrete Mathematics for Mico

Question

Exercise # 2 A committee composing of six members naming Ana, Ben, Cora, Dina, Elphie and Francis is to select a chairperson, secretary and a treasurer. d. In how many ways can they select the chairperson, secretary and treasurer? e. In how many ways can they choose if either Ana or Ben must be the chairperson? f. In how many ways ca they choose if Elphie must hold one of the positions? g. In how many ways can they choose if Dina and Francis must hold a position?

Answer 1

d.

$n=C^3_6=\frac{6!}{3!3!}=20$ ways

e.

$n=2C^2_5=\frac{2\cdot5!}{2!3!}=20$ ways

f.

$n=C^2_5=\frac{5!}{2!3!}=10$ ways

g.

$n=C^1_4=\frac{4!}{3!}=4$ ways