Six dice are thrown simultaneously. The probability that all of them show different faces, is

\frac{1}{6^{5}}

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\frac{6!}{6^{6}}

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\frac{1}{{6!}}

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\frac{5!}{6^{6}}

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Solution

The correct option is A $\frac{6!}{6^{6}}$
total number of possibilities = $6^{6}$
and Required case $\Rightarrow$ Arrange $1, 2, 3, 4, 5, 6$ on $6$ dices
$= 6!$ ways
$∴$ required probability = $\frac{6!}{6^{6}}$

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Six dice are thrown simultaneously. The probability that all of them show different faces, is

The correct option is A 6!66total number of possibilities = 66and Required case ⇒ Arrange 1,2,3,4,5,6 on 6 dices =6! ways ∴ required probability = 6!66

The correct option is A $\frac{6!}{6^{6}}$
total number of possibilities = $6^{6}$
and Required case $\Rightarrow$ Arrange $1, 2, 3, 4, 5, 6$ on $6$ dices
$= 6!$ ways
$∴$ required probability = $\frac{6!}{6^{6}}$