Question

I have some combination questions:
(a) The Mathematics departmental office has the following stock of
dry-erase markers: 7 Red, 4 Navy blue, 6 Green, 8 Black. They are
to be distributed, 1 apiece, to the 25 members of the department. How many outcomes are possible?
(b) The Chemistry departmental office has 800 black dry-erase markers. The 25 members of the department may take as many as they like. If 46 markers are taken the first day, how many different distributions to the faculty members are possible?

Answer 1

(c) Repeat (b) with the added stipulation that each faculty member
took at least one marker.
(d) The Physics departmental office has the following stock of dry-erase markers: 400 Red, 200 Green, 200 Black. The 25 members
of the department may take as many as they like. If 46 Red, 3 Green, and 27 Black markers are taken the first day, how many different distributions to the faculty members are possible?

Answer 2

for a) I found

C(25,8)*C(17,7)*C(10,6)*C(4,4)

Answer 3

@amistre64

Answer 4

@Zarkon , @TuringTest

Answer 5

for b) I found
\[\frac{70!}{46!*24!}\]

Answer 6

outcomes = arrangement...i think

Answer 7

for c) my result is

\[\frac{45!}{25!*20!}\]

Answer 8

yes @Yahoo!

Answer 9

So..... npr

Answer 10

outcomes= how many ways we have to do that..

Answer 11

@eliassaab

Answer 12

why we need to multiply by 25!

Answer 13

do you think color is important..

Answer 14

let say we have 2 red 3 blue 4 green pen and we wanna give them 9 children ( 1 each of them)
and lets say we have 9 black pen and we wanna give them 9 children (( 1 each of them)
are thees the same situation or different

Answer 15

Diffrent

Answer 16

so we need to multiply by 25! then.. because we have different color pens..

Answer 17

oh repeated permutation, so in our case 25!/(8!7!6!4!) right..

Answer 18

it makes sense..thanks..

Answer 19

no I don't (:

Answer 20

@eliassaab is...very strong in permutation and combination

Answer 21

for b) is 800 important?

Answer 22

but there is only one way color is the same..

Answer 23

every members can take only one pen, one member cannot take 0 or 2,3,.....25 pens

Answer 24

the question is whether one can choose only only 1 red from the 7

Answer 25

oh you are asking they are in the same box and mixed or they have their own box ( each color)

if this is your question I thought first condition..

Answer 26

this question really confuses..))

Answer 27

Wat Did u understand frm the question

Answer 28

1st and 2nd option are the same or not..

Answer 29

we are not arranging them we are choosing them, are we?

Answer 30

the question asks for...possible outcome...

Answer 31

Thanks for your help, I gotta go to library get a book about this topic.. see you later (:

Answer 32

I'm going to Office Depot to buy my own markers!

Answer 33

but thees are free, choose one :P

Answer 34

@eliassaab can you look at my question, I am stuck

Answer 35

a)
\[
\frac{25!}{7! 4! 6!
8!}=4417238826000
\]
Which the same as you got/

Answer 36

thanks..

Answer 37

@satellite73 can you look at my question, if you are
not busy