A fair six-faced die is rolled 12 times. The | vedclass

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(C) The total number of outcomes when a die is rolled $12$ times is $6^{12}$.We want each of the $6$ faces to appear exactly $2$ times.This is a multi

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$\frac{12!}{2^{6} 6^{12}}$

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(C) The total number of outcomes when a die is rolled $12$ times is $6^{12}$.We want each of the $6$ faces to appear exactly $2$ times.This is a multinomial distribution problem where we arrange $12$ items into $6$ groups of size $2$ each.The number of ways to distribute $12$ outcomes such that each face appears twice is given by the multinomial coefficient:$\frac{12!}{2! 2! 2! 2! 2! 2!} = \frac{12!}{(2!)^6} = \frac{12!}{2^6}$.Therefore, the required probability is:$P = \frac{12!}{2^6 	imes 6^{12}}$.

$X=x$	$1$	$2$	$3$
$P(X=x)$	$1/5$	$2/5$	$2/5$

$A$ fair six-faced die is rolled $12$ times. The probability that each face turns up exactly twice is equal to:

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