25. Seven students (Catherine, Jim, Jerome, Lucia, Lisa, Melinda, and Dave) are entered in a debate contest.

Question

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: ________________________

Answer 1

Fulfill the obligations first
a) XLXXXXX -----> Numbe of ways = 6*1*5*4*3*2*1 = 720
b) LXXXXDX -----> Number of ways = 1*5*4*3*2*1*1 = ...
c) 3 boys, then 4 girls: BBBGGGG -----> 3*2*1*4*3*2*1 = ....
d) 4 girls and 3 boys: GGGGBBB -----> ......... = ....
e) ........

Answer 2

Hi Reiny,
I was solving them as following:

i) Lucia must go second:
_ L _ _ _ _ _ = 6! =6x5x4x3x2x1 = 720
ii) Lisa must go first and Dave must go second to last:
L _ _ _ _ D _ = 5! =5x4x3x2x1 = 120
iii) All of the boys go first followed by the girls:
BBBGGGG = 3!4! =(3x2x1)(4x3x2x1) = (6)(24) = 144
iv) All of the girls go first followed by the boys:
GGGGBBB = 4!3! =(4x3x2x1)(3x2x1) = (24)(6) = 144
v) Females and males alternate with a female going first:
GBGBGBG = 4!3! =(4x3x2x1)(3x2x1) = (24)(6) = 144

Anyone else have any edits as well, I would highly appreciate it.
Thanks for your time.

Answer 3

Don't you realize that is exactly what I was doing?

Answer 4

yeah thats what I thought you were doing. I was just talking about question e.) as your answer was ........, I just got confused.
Thankyou so much for your time and effort, I really appreciate it.