Using the Fundamental Counting Theorem, it is found that there are 1000 possible numbers that Lina could pick.
What is the Fundamental Counting Theorem?
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:
- The number is more than 5000, hence the first digit can be 5, 6, 7, 8 or 9, hence [tex]n_1 = 5[/tex].
- The second digit is prime, that is, 2, 3, 5 or 7, hence [tex]n_2 = 4[/tex].
- For the third digit, there are no restrictions, hence [tex]n_3 = 10[/tex].
- The number is odd, hence the fourth digit can be 1, 3, 5, 7 or 9, hence [tex]n_4 = 5[/tex].
Hence the number of combinations is given by:
N = 5 x 4 x 10 x 5 = 1000
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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