Discrete Mathematics Answers

A committee of 12 is to be selected 1 cm 10 cm men and women in how many ways can the selection be carried out if
A)there are no restrictions?
B)there must be six men and six women
C) there must be an even number of women?
D) there must be more women than men
E)there must be at least eight men?

veryfy that r->(q->r)(p->q)->p->r)ia a tautology

construction the truth table for each of the following compound statements where p.q denote primitive statements
a. (p.->q)->p
b. (P->q)->(p->q)
c. (p->q) (q->p)->p->r)

determine the coefficient of x"y"in the expansions of
a) (x+y)12
b) (x+2y)12
c) (2x-3y)12

given a graphe with trivial automorphism group. Wat is the smallest subgraph with trivial automorphism group? Can we fid all or somme of thes subgraphs?

The State department is trying to identify an individual who speaks Farsi to fill a foreign embassy position. They have determined that that 4% of the applicant pool are fluent in Farsi.
A) If applicants are contacted randomly how many individuals can they expect to interview in order to find one fluent in Farsi?
B)What is the probability that they will interview more than 25 before they find one who speaks Farsi? More than 40?