- anonymous

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

- chestercat

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- anonymous

i think you have to grind it til you find it

- anonymous

sorry i was away

- anonymous

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

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## More answers

- anonymous

i have tried a number of times but cant solve it

- anonymous

cant break down the cases correctly

- anonymous

i assume

- 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

- anonymous

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

- anonymous

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

- 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

- anonymous

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

- anonymous

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

- anonymous

damn i forgot 3 dimes!!

- Zarkon

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

- anonymous

I will try to add them up and see

- anonymous

add another 10
what is the quick way for my benefit

- Zarkon

which gives a total of 104

- Zarkon

you can also look at it this way...

- anonymous

now i get to learn something

- 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

- anonymous

yes much snappier

- Zarkon

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

- anonymous

these few are killing me

- anonymous

104 is correct

- anonymous

yes well that would really be magic

- anonymous

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

- anonymous

?:)

- anonymous

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

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