## anonymous 4 years ago I have some questions regarding combinations in finite. Here is my first one I am stumped on: Select 3 coins, but assume that there are 5 dimes, 3 nickels, and 2 quarters. In How many possible ways can the selection be made so that the value of the coins is AT LEAST 25 cents?_______________________________ Any help? Formulas have not done me so well

1. anonymous

i think you have to grind it til you find it

2. anonymous

sorry i was away

3. anonymous

oh good so i am less embarrassed. you have to work in cases

4. anonymous

i have tried a number of times but cant solve it

5. anonymous

cant break down the cases correctly

6. anonymous

i assume

7. anonymous

1) two quarters one dime only one way to select two quarters, 5 choices for the dime, so 5 in that case 2) two quarters one nickel, 3 choices for the nickel so 3 ways in that case

8. anonymous

3) one quarter two dimes $2\times \dbinom{5}{2}=2\times 10=20$

9. anonymous

4) one quarter two nickels $2\times 3=6$ 5) one quarter one dime one nickel $2\times 3\times 5=30$

10. anonymous

and finally two dimes and a nickel $10\times 3=30$ think that is all, so if we add them up we should get the right answer

11. anonymous

@zarkon, you got a snap way to do this, or it it just grind it out?

12. anonymous

wow i did not break the cases down enough I will check and see if it is right

13. anonymous

damn i forgot 3 dimes!!

14. Zarkon

I do have a quicker way...but it is goog to do it this way...you also nee 3 dimes I believe

15. anonymous

I will try to add them up and see

16. anonymous

add another 10 what is the quick way for my benefit

17. Zarkon

which gives a total of 104

18. Zarkon

you can also look at it this way...

19. anonymous

now i get to learn something

20. Zarkon

there are $_{10}C_{3}=120$ ways to pick the 3 coins... only NNN and 2nickles and a dime are less than 25 cents 120-1-15=104

21. anonymous

yes much snappier

22. Zarkon

I don't see a way to do it without some cases

23. anonymous

these few are killing me

24. anonymous

104 is correct

25. anonymous

yes well that would really be magic

26. anonymous

thank you so much I have some more that I am stumped as well if you want to crack them

27. anonymous

?:)

28. anonymous

post a new thread, you will get lots of answers i am sure