No. 11!

Calvin and Arron throw one dice for a stake of \(11$\) which is to be won by the player who first throws a six on the dice. The game ends when the stake is won either by Calvin or by Arron. The first throw is of Calvin. If the probability that Calvin wins the stake is \(x\) and that of Arron is \(y\), then find the value of \((11x)!-(11y)!\)

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