Question

A fiar six sided die is rolled 6 times what is the probabilty of getting a unique number

Answer 1

6/6*5/6*4/6*3/6*2/6*1/6=720/46656

Answer 2

Number of times you roll the dice = 6
$= > n(s) = {6}^{6}$
You need to get a 1 at first chance
- a 2 at second
- a 3 at third
... and what's left at each chance is gonna come at next

So, we're gonna count the number of ways in which we can form a six-digit number with ( 1, 2, 3, 4, 5, 6 ) without repeating each digit twice, yeah, cause in the end... that's the number of patterns in which our motive can be achieved

$= > desired \: ways = 6 \times 5 \times 4 \times 3 \times 2 \times 1$
Hence, we arrive at the Desired Probability as :
$p(event) = \frac{n(event)}{n(s)} \\ = > desired \: probability = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{ {6}^{6} }$
Hence, your answer is :
$p(event) = \frac{720}{46656} = \frac{5}{324}$