A die is rolled 10 times. What is the probability that 1, 2 and 3 occur once each, 4 and 5 occur twice each, and 6 occurs 3 times?

Answer: 0.0025

Step-by-step 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