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junior college 2 | H2 Maths
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Sally Tan
Sally Tan

junior college 2 chevron_right H2 Maths chevron_right Singapore

Hello, please help me with ii of this question, thank you!

Date Posted: 3 years ago
Views: 759
J
J
3 years ago
You just need to divide the answer in part i) by 4!

The four players are unique and are distinguishable but the stacks of cards are indistinguishable.
J
J
3 years ago
Eg.

One of the possible distributions :

Player 1 → card 1,2,3
Player 2 → card 4,5,6
Player 3 → card 7,8,9
Player 4 → card 10,11,12

There are 4 possible choices of players to assign cards 1,2,3 , followed by 3 possible choices for cards 4,5,6, followed by 2 possible choices for cards 7,8,9 and 1 only possible choice for 10,11,12

4×3×2×1 = 4! = 24


The above would be different and distinguishable from :

Player 3 → card 1,2,3
Player 4 → card 4,5,6
Player 2→ card 7,8,9
Player 1 → card 10,11,12


But for stacks , they have no unique identity. So they are not distinguishable and the above two would be considered repeated cases.

We have to get rid of repeated cases so we must divide by 4!

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J's answer
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