A Trillionaire might do this...
Someone recently opened a new doughnut shop in town. The first set they offered was something called the Dusted Special, which cost $36.
It consisted of your selection of 24 doughnuts from 12 different types, mixed and matched in any way you choose. e.g. you might have 12 chocolate, 4 frosted, and 8 jelly doughnuts
Question:
If someone were to purchase all the possible 'Dusted Specials', how much would they end up paying?
Notes:
Order doesn't matter (That is, combinations rather than permutations)
You should be able to solve this problem with just a bit of creativity + knowledge of factorials
Hints:
It isn't 12^24 or 24^12
It isn't C(24, 11)
IMPORTANT:
If your answer is x dollars, submit your answer as x/100
The answer is 150201324.
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1 solution
Imagine selecting your Dusted Special, and ordering your doughnuts by type (A,B,C,D, etc.). Then, place a plastic doughnut ( P ) between each type of doughnut.
In the end, you might have something that looks like AAA P BB P CCCCCCC P DDDD P E P F P G P [No H] P II P J P K P L.
Then, my removing all the edible doughnuts, you'd get _ _ _ P _ _ P _ _ _ _ _ _ _ P _ _ _ _ P _ P _ P _ P P _ _ P _ P _ P _
All in all, there are 35 slots to put the rubber doughnuts in (you include the first and last because you could have no A's or L's) and 11 P doughnuts to place.
Therefore, your answer would be 2 4 ! ∗ 1 1 ! 3 5 ! , which works out to 417225900 combinations. Multiplying by 36 then dividing by 100 gives an answer of 150201324 (hundreds of dollars).