Question

Lina picks a 4 digit number.

Answer 1

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 $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

• The number is more than 5000, hence the first digit can be 5, 6, 7, 8 or 9, hence $n_1 = 5$.

• The second digit is prime, that is, 2, 3, 5 or 7, hence $n_2 = 4$.

• For the third digit, there are no restrictions, hence $n_3 = 10$.

• The number is odd, hence the fourth digit can be 1, 3, 5, 7 or 9, hence $n_4 = 5$.

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 brainly.com/question/24314866

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