## anonymous 4 years ago 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?

1. anonymous

(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?

2. anonymous

for a) I found C(25,8)*C(17,7)*C(10,6)*C(4,4)

3. anonymous

@amistre64

4. anonymous

@Zarkon , @TuringTest

5. anonymous

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

6. anonymous

outcomes = arrangement...i think

7. anonymous

for c) my result is $\frac{45!}{25!*20!}$

8. anonymous

yes @Yahoo!

9. anonymous

So..... npr

10. anonymous

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

11. anonymous

@eliassaab

12. anonymous

why we need to multiply by 25!

13. anonymous

do you think color is important..

14. anonymous

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

15. anonymous

Diffrent

16. anonymous

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

17. anonymous

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

18. anonymous

it makes sense..thanks..

19. anonymous

no I don't (:

20. anonymous

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

21. anonymous

for b) is 800 important?

22. anonymous

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

23. anonymous

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

24. anonymous

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

25. anonymous

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..

26. anonymous

this question really confuses..))

27. anonymous

Wat Did u understand frm the question

28. anonymous

29. anonymous

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

30. anonymous

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

31. anonymous

32. anonymous

33. anonymous

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

34. anonymous

but thees are free, choose one :P

35. anonymous

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

36. anonymous

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

37. anonymous

thanks..

38. anonymous

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