Respuesta :
Using the fundamental counting principle, it is found that 15500 different passwords are possible.
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The fundamental counting principle states that if there are p ways to do one things, and q ways to do other thing, and they are independent, there are p*q ways to do both things.
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- For each digit, there are 10 ways.
- For each vowel, there are 5 ways.
- The digits and the vowels are independent, thus, the fundamental counting principle is applied.
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- With one vowel followed by two digits, there are [tex]5 \times 10^2 = 5 \times 100 = 500[/tex] passwords.
- With two vowels followed by two digits, there are [tex]5^2 \times 10^2 = 25 \times 100 = 2500[/tex] passwords.
- With three vowels followed by three digits, there are [tex]5^3 \times 10^2 = 125 \times 100 = 12500[/tex] passwords.
- In total, there are [tex]500 + 2500 + 12500 = 15500[/tex] passwords.
A similar problem is given at https://brainly.com/question/23855405
