Four Kaboobly Dooists come to your house
A Kaboobly Dooists is a person who does a lot of Kaboobly Doo.
One winter evening, four Kaboobly Dooists, Alice, Bob, Charles and Dick come to see you. Unfortunately you had nothing for them except 5 apples, 4 oranges, 3 mangoes. And you do not wish to spend all 12 of the fruits on them as you wish to keep 8 for yourself. So, you give a total of 4 fruits, one fruit to each of them.
In how many ways can you do this?
The answer is 80.
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2 solutions
Oh boy, that's awesome!
why is it not solved as: alice can get 1 of 12 fruits =12 bob can get 1 of the remaining 11 fruits=11 charles can get 1 of the remaining 10 fruits=10 and dick can get 1 of the remaining 9 fruits=9 which makes 12+11+10+9=42 ways.
same thought for me
Mathematica Code
Permutations[{a,a,a,a,a,o,o,o,o,m,m,m}, {4}]//Length
Want to see the casework answer?
1 pair:
2 ! ⋅ 1 ! 3 ( 2 2 ) ⋅ 4 ! = 3 6
2 pairs:
2 ! ⋅ 2 ! 3 ⋅ 4 ! = 1 8
All the same:
Just 2, {a,a,a,a} and {o,o,o,o}
3 of the same:
3 ! ⋅ 1 ! ( 3 ⋅ 2 ) 4 ! = 2 4
36 + 18 + 2 + 24 = 80
A big thanks to bobbym none for the solutions
Another way here.
First 3 persons can choose 3 fruits in 2 7 ways.
Now for 2 6 cases the last person can choose any of the 3 types of fruit. So, 2 6 ∗ 3 = 7 8
For 1 case(when all 3 mangoes have been already chosen) the last person can choose only 2 types. So, 1 ∗ 2 = 2
7 8 + 2 = 8 0
What's Kaboobly Doo?
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It is a very hard concept but I recommend you read this
I hope you liked the problem. It has got nothing to do with Kaboobly Doo but it surely makes the problem more interesting
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When I googled 'Kaboobly Doo' that link came up first. But the link doesn't work for me. Could you give a very short intro?
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kaboobly doo, def: Something usually posted by T to annoy and vex ole m. It is an outlandish comment such that only Gilligan or a Curly could think of.
Kaboobly Doo is an adjective. It could be used to refer to things that make no sense.
Example of Usage: @Will Cassels posts Kaboobly Doo problems.
Sometimes it can also be used as an interjection like this:
Kaboobly Doo!
I suspect Kaboobly Doo has deeper meanings of which I am not aware
I'll tag you here: @bobbym none
I think that question is not clear. Are apples distinguishable between each other or not ? The same for oranges and mangoes . Is this important what fruit got Alice, Bob, Charles and Dick ? For example 14 can be answer (a,a,a,a), (a,a,a,o), (a,a,a,m), (a,a,o,o), (a,a,o,m), (a,a,m,m), (a,o,o,o), (a,o,o,m), (a,o,m,m), (a,m,m,m), (o,o,o,o), (o,o,o,m), (o,o,m,m), (o,m,m,m). And from above sets it is unimportant which fruit got person, just I save 8 fruit for me and distribute 4.
For each of the 4 persons you have 3 options, apple, orange or mango. The answer should be 3 x 3 x 3 x 3 = 81. But if you give 1 mango each to the 1st, 2nd and the 3rd person, then for the 4th person you will be left with 2 options only. So, the final and correct answer should be 81 - 1 = 80