hw help

[erica123]

Hi, I need help with these 3 problem

3) 52 divided among 4 players. Each player may receive between 0 and 52 cards. How many outcomes?

4) 52 cards are divided into 4 piles. The piles are not necessarily of equal size (but each pile is non-empty). How many outcomes?

5) 52 cards are dipped in black ink (no longer distinguishable). How many ways to divide them into 4 equal piles?

6) 52 black cards (not distinguishable) are divided among 4 players (not necessarily equally(. Each player must receive at least 1 card. How many outcomes are possible?

 

[Deleted member 4993]

Hi, I need help with these 3 problem

3) 52 divided among 4 players. Each player may receive between 0 and 52 cards. How many outcomes?

4) 52 cards are divided into 4 piles. The piles are not necessarily of equal size (but each pile is non-empty). How many outcomes?

5) 52 cards are dipped in black ink (no longer distinguishable). How many ways to divide them into 4 equal piles?

6) 52 black cards (not distinguishable) are divided among 4 players (not necessarily equally(. Each player must receive at least 1 card. How many outcomes are possible?

First figure out - how many cards would each player get.

Please show us what you have tried and exactly where you are stuck.

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[pka]

Hi, I need help with these 3 problem
3) 52 divided among 4 players. Each player may receive between 0 and 52 cards. How many outcomes?
4) 52 cards are divided into 4 piles. The piles are not necessarily of equal size (but each pile is non-empty). How many outcomes?
5) 52 cards are dipped in black ink (no longer distinguishable). How many ways to divide them into 4 equal piles?
6) 52 black cards (not distinguishable) are divided among 4 players (not necessarily equally(. Each player must receive at least 1 card. How many outcomes are possible?

#3. Is simply \(4^{52}\) that is the number of ways of placing \(n\) distinguishable objects into \(k\) distinguishable cells: \(k^n\).
The other three involve Stirling Numbers of the Second order: \(\mathcal{S}_k^{(n)}\)
The topic of Stirling Numbers can take up an entire chapter of an textbook.