Permutations and combinations – MathOverflow


Seven students (Catherine, Jim, Jerome, Lucia, Lisa, Melinda, and Dave) are entered in a debate contest.
a) In how many ways can they give their arguments if the following conditions must be met?
i) Lucia must go second: _________________________________________________
ii) Lisa must go first and Dave must go second to last: __________________________
iii) All of the boys go first followed by the girls: _______________________________
iv) All of the girls go first followed by the boys: _______________________________
v) Females and males alternate with a female going first: ________________________