Hello friends

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bibidi_skibidi

5 posts

bibidi_skibidi

#1 h Apr 15, 2025, 4:04 AM • 2 Y

Y by aidan0626, GodGodGodGodGoose

Now unfortunately I don't know the difficulty of the problems posted here but I'll try to replicate:

Bob has 20 apples and 19 oranges. How many ways can he split the fruits between 7 people if each person must have at least 1 apple and 2 oranges?

After looking at the other posters I realized just how bashy this is

Also I can only edit this message for now since new AoPS users can only send 6 messages every day

This post has been edited 1 time. Last edited by bibidi_skibidi, Apr 15, 2025, 4:19 AM

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aidan0626

1875 posts

aidan0626

#2 h Apr 15, 2025, 4:10 AM

Y by

Hi

This is standard stars and bars, there are $\binom{19}{6}$ ways to split the apples and $\binom{11}{6}$ ways to split the oranges, and you just multiply those two together to get the final answer.

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Soupboy0

344 posts

Soupboy0

#3 h Apr 15, 2025, 4:11 AM

Y by

bro i got sniped :rotfl:

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maxamc

568 posts

maxamc

#4 h Apr 15, 2025, 4:11 AM

Y by

aidan0626 wrote:

Hi

This is standard stars and bars, there are $\binom{19}{6}$ ways to split the apples and $\binom{11}{6}$ ways to split the oranges, and you just multiply those two together to get the final answer.

Wolfram Alpha gives 12534984 as our final answer (impossible to compute)

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fluffyyyyyyy

1 post

fluffyyyyyyy

#5 h Apr 15, 2025, 4:19 AM

Y by

hello sabko

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Leeoz

178 posts

Leeoz

#6 h Apr 15, 2025, 6:39 AM

Y by

maxamc wrote:

aidan0626 wrote:

Hi

This is standard stars and bars, there are $\binom{19}{6}$ ways to split the apples and $\binom{11}{6}$ ways to split the oranges, and you just multiply those two together to get the final answer.

Wolfram Alpha gives 12534984 as our final answer (impossible to compute)

its not "impossible"

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Thayaden

1361 posts

Thayaden

#7 h Apr 15, 2025, 5:45 PM

Y by

bibidi_skibidi wrote:

Now unfortunately I don't know the difficulty of the problems posted here but I'll try to replicate:

Bob has 20 apples and 19 oranges. How many ways can he split the fruits between 7 people if each person must have at least 1 apple and 2 oranges?

After looking at the other posters I realized just how bashy this is

Also I can only edit this message for now since new AoPS users can only send 6 messages every day

Start by giving away the required fruit this leaves 18 fruit for grabs namely 13 ap0pels and 5 oranges we set up stars and bars for extras and get (13+6)! but yet no oranges is diffrent from another orange and there are 5! ways to arage oranges and 13! ways to arange appels and 6! ways to arange bars so I think our answer is $\boxed{\frac{(18+6)!}{5!13!6!}}$ is what I got

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maxamc

568 posts

maxamc

#8 h Apr 16, 2025, 12:34 AM

Y by

Thayaden wrote:

bibidi_skibidi wrote:

Now unfortunately I don't know the difficulty of the problems posted here but I'll try to replicate:

Bob has 20 apples and 19 oranges. How many ways can he split the fruits between 7 people if each person must have at least 1 apple and 2 oranges?

After looking at the other posters I realized just how bashy this is

Also I can only edit this message for now since new AoPS users can only send 6 messages every day

Start by giving away the required fruit this leaves 18 fruit for grabs namely 13 ap0pels and 5 oranges we set up stars and bars for extras and get (13+6)! but yet no oranges is diffrent from another orange and there are 5! ways to arage oranges and 13! ways to arange appels and 6! ways to arange bars so I think our answer is $\boxed{\frac{(18+6)!}{5!13!6!}}$ is what I got

Your answer is 1153218528, not equal to my Wolfram Alpha answer described above, unfortunately wrong I think.

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BS2012

1025 posts

BS2012

#9 h Apr 16, 2025, 12:49 AM

Y by

its just Solution sketch which is the same as the 2nd post

This post has been edited 3 times. Last edited by BS2012, Apr 16, 2025, 12:52 AM

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giratina3

495 posts

giratina3

#10 h Apr 16, 2025, 2:57 AM

Y by

This is not bashy at all if you know Stars and Bars. I would recommend reading the later sections of Intro to Counting and Probability for more information.

This post has been edited 1 time. Last edited by giratina3, Apr 16, 2025, 2:57 AM

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