anonymous
  • 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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
i think you have to grind it til you find it
anonymous
  • anonymous
sorry i was away
anonymous
  • anonymous
oh good so i am less embarrassed. you have to work in cases

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anonymous
  • anonymous
i have tried a number of times but cant solve it
anonymous
  • anonymous
cant break down the cases correctly
anonymous
  • anonymous
i assume
anonymous
  • 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
  • anonymous
3) one quarter two dimes \[2\times \dbinom{5}{2}=2\times 10=20\]
anonymous
  • anonymous
4) one quarter two nickels \[2\times 3=6\] 5) one quarter one dime one nickel \[2\times 3\times 5=30\]
anonymous
  • 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
  • anonymous
@zarkon, you got a snap way to do this, or it it just grind it out?
anonymous
  • anonymous
wow i did not break the cases down enough I will check and see if it is right
anonymous
  • anonymous
damn i forgot 3 dimes!!
Zarkon
  • Zarkon
I do have a quicker way...but it is goog to do it this way...you also nee 3 dimes I believe
anonymous
  • anonymous
I will try to add them up and see
anonymous
  • anonymous
add another 10 what is the quick way for my benefit
Zarkon
  • Zarkon
which gives a total of 104
Zarkon
  • Zarkon
you can also look at it this way...
anonymous
  • anonymous
now i get to learn something
Zarkon
  • 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
  • anonymous
yes much snappier
Zarkon
  • Zarkon
I don't see a way to do it without some cases
anonymous
  • anonymous
these few are killing me
anonymous
  • anonymous
104 is correct
anonymous
  • anonymous
yes well that would really be magic
anonymous
  • anonymous
thank you so much I have some more that I am stumped as well if you want to crack them
anonymous
  • anonymous
?:)
anonymous
  • anonymous
post a new thread, you will get lots of answers i am sure

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