Answer: 0.0025
Explanation:
Given that 1,2,3 occur once each, 4 and 5 occur twice each, 6 occurs 3 times,
A possible outcome we have is [1,2,3,4,4,5,5,6,6,6]
Total number of ways to arrange this outcome is 10! Ways.
Since 1 occurs once, number of ways we can arrange that just 1 is 1!
Since 2 occurs once, number of ways we can arrange that just 2 is 1!
Since 3 occurs once, number of ways we can arrange that just 3 is 1!
Since 4 occurs twice, number of ways we can arrange that just 4 is 2
Since 5 occurs twice, number of ways we can arrange that just 5 is 2!
Since 6 occurs on thrice, number of ways we can arrange that just 6 is 3!
Hence, total number of ways this our particular outcome can be arranged is 10!/(1!* 1!* 1!* 2!* 2!* 3!)
=3628800/24
=151200
However, the total number of sample space for this die is 6^10 = 60466176
Hence, the probability of 1, 2 and 3 occur once each, 4 and 5 occur twice each, and 6 occurs 3 times = 151200/60466176 = 0.0025