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Card Orders

Consider a deck of 120 cards, 60 red and 60 black. From a shuffled
deck, which of the following is most likely when dealing the cards?
- Alternating red, black, red, black, ...
- Alternating 2 reds, 2 blacks, 2 reds, 2 blacks, ...
- Alternating 3 reds, 3 blacks, 3 reds, 3 blacks, ...
- Alternating 4 reds, 4 blacks, 4 reds, 4 blacks, ...
- Alternating 5 reds, 5 blacks, 5 reds, 5 blacks, ...
- Alternating 6 reds, 6 blacks, 6 reds, 6 blacks, ...

Assigning the least likeliest option a value of 1, how much more likely
is each other option?
Source: Original.

Solution

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