Question

Can someone please help me with this problem. Ive been trying to figure it out ALL DAY and posting it up.

150 freshmen, 125 sophomores, 100 juniors, and 75 seniors must select 4 of its member for student council. How many types of councils are possible if the following condition is satisfied? *I want actual numbers for this problem please!

a) One senior is President and one senior is Vice President
b) One senior is President and one Junior is Vice President
c) The majority of its members are sophomores
d) The council has exactly one senior and one freshman.

Answer 1

what are different posts?

Answer 2

how many ways to fill the positions right?

as opposed to how many ways can the same group of people be selected without regard for position?

Answer 3

spose there are just 6 choices and 3 positions to fill:

6 pick 3 gives as all the ways to fill the positions:

6*5*4 = 120 possible ways to do it; but, this takes order as seperate counts; ABC is a different count then BCA.

Answer 4

Yes how many way to fill the positions.

Answer 5

6 pick 3
------- is the number of ways to group the people when
3! mixed orders count the same.

ABC is the same count as CAB is the same count as BCA etc...

Answer 6

sen. oth. oth. sen.
--- ---- --- ---
75 375 374 74 ; if i see it right for 'a'

Answer 7

Is this for a and b?

Answer 8

no; thats just for a :) if i see it right that is; im unsure if we count the seniors in with the others for 2 and 3 or not

Answer 9

sen jun oth oth
--- --- --- ---
75 100 275 274 ; would be my guess for 'b'

Answer 10

and we multiply these number together

Answer 11

oh ok. So would B be kinda the same set up?

Answer 12

?

Answer 13

similar yes; but I have to read up on if I am actually doing it right, unless you have a way to verify my answers :)

Answer 14

No I don't have a way to verify these answers

Answer 15

i think i have an error, the logic being this:

total population = all students

sen 75 ; total pop is minus 1 student now
sen 74 ; total pop is minus 2 student now
any total pop -2
any total pop -3

Answer 16

total pop = 150+125+100+75 = 450

150 fm, 125 sophs, 100 jrs, and 75 srs

We want 2 seniors for "a":

75 *74 *448 *447
............................................

a sr and a jr for "b"

75 *100 *448 *447
.............................................

majority of sophs; at least 3 of them for "c"

125 *124 *123 *447
..........................................

exactly one sr and exactly one fmn for "d"

75 * 150* 225 *224

Answer 17

I think for a) it is 10 (sen,sen (two given) together with sensen OR ff OR ss OR jj OR fs OR fj OR sj OR sens OR senf OR senj) (order doesn't matter).

I don't think the titles are important only the type and you only can select four people.

You can do other similar (someone else can).

Answer 18

?.? Based on the above for a) 75 *74 *448 *447 <== this says the order of the other two members matters.... I agrees with 'estudier' that the order doesn't matter....
so a) 75 *74 *448C2= a huge # -.-
b) 75*100*448C2 = another huge # -.-;
c) not sure about this one because it's annoying!!! my guess it's = 364831250 how? toooo long to explain @.@
d) 75*150*225C2 = another huge # =.=

Answer 19

It doesnt say suggest order is important; it just puts the offices in order to fill them.

Pres * VP *other *other ; is all it does to make sorting the
matter easier to follow

Answer 20

Pres requires a sen. ; fill it first
VP requires a sen. ; fill it next

the others are then able to fill in with whatever is left out of th etotal population