Henry Ernest Dudeney/Puzzles and Curious Problems/315 - Arranging the Dominoes/Solution

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Puzzles and Curious Problems by Henry Ernest Dudeney: $315$

Arranging the Dominoes
The number of ways the set of $28$ dominoes may be arranged in a straight line, in accordance with the original rule of the game,
left to right and right to left, in any arrangement counting as different ways,
is $7 \, 959 \, 229 \, 931 \, 520$.
After discarding all dominoes bearing a $5$ or a $6$, how many ways may the remaining $15$ dominoes be so arranged in a line?


Solution

There are $126 \, 720$ ways to arrange $15$ dominoes as described.


Proof


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Sources

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