Using the Fundamental Counting Theorem, it is found that there is a 0.2 = 20% probability of choosing a random number that starts with 9 from this group.
It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, we have that:
Then, the total number is:
N = 5 x 4 x 8 x 7 x 6 x 5 = 33600.
Starting with 9, we have that:
Then:
N9 = 1 x 4 x 8 x 7 x 6 x 5 = 6720.
A probability is given by the number of desired outcomes divided by the number of total outcomes, hence:
p = N9/N = 6720/33600 = 0.2.
0.2 = 20% probability of choosing a random number that starts with 9 from this group.
To learn more about the Fundamental Counting Theorem, you can check https://brainly.com/question/24314866