Respuesta :
The number of combinations is given by 1000
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,........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 n_2\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
To learn more about the Fundamental Counting Theorem at:
brainly.com/question/24314866
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