Answer:
the probability that 5 of each of the values 1, 2, 3, 4, 5, 6 appear is 0.0004
Explanation:
Given that;
group of dice thrown (n) = 30
number of samples n(S) = 6³⁰
the probability that 5 of each of the values 1, 2, 3, 4, 5, 6 appear = ?
let A rep the event that 5 out of each of the values 1, 2, 3, 4, 5, 6 appear.
number of ways that 30 dice can be thrown is 30!
now, In the thirty throws from 1 to 30, there are;
FIVE 1's, FIVE 2's, FIVE 3's, FIVE 4's, FIVE 5's, FIVE 6's characters to assign the dice.
which means n(A) = 30! / 5!5!5!5!5!5!
Now the probability that 5 of each of the values 1, 2, 3, 4, 5, 6 appear will be;
P(A) = 30!/5!5!5!5!5!5! / 6³⁰
P(A) = 30! / (5!)⁶ (6³⁰)
P(A) = 0.0004
Therefore the probability that 5 of each of the values 1, 2, 3, 4, 5, 6 appear is 0.0004