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

Question

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

anonymous · Answer

i think you have to grind it til you find it

anonymous · Answer

sorry i was away

anonymous · Answer

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

anonymous · Answer

i have tried a number of times but cant solve it

anonymous · Answer

cant break down the cases correctly

anonymous · Answer

i assume

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

damn i forgot 3 dimes!!

zarkon · Answer

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

anonymous · Answer

I will try to add them up and see

anonymous · Answer

add another 10
what is the quick way for my benefit

zarkon · Answer

which gives a total of 104

zarkon · Answer

you can also look at it this way...

anonymous · Answer

now i get to learn something

zarkon · Answer

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

anonymous · Answer

yes much snappier

zarkon · Answer

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

anonymous · Answer

these few are killing me

anonymous · Answer

104 is correct

anonymous · Answer

yes well that would really be magic

anonymous · Answer

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

anonymous · Answer

?:)

anonymous · Answer

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