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- A password consists of 4 letters, where each letter can be either a vowel (a, e, i, o, u) or a consonant. However, consecutive letters cannot be the same. How many differ
A password consists of 4 letters, where each letter can be either a vowel (a, e, i, o, u) or a consonant. However, consecutive letters cannot be the same. How many different passwords are possible?
25,000
36,450
15,600
56,000
Answers (1)
For the first position, there are 5 options (vowels: a, e, i, o, u) and 21 options (consonants) available.
For the second position, if the first letter is a vowel, there are 4 options left for a vowel (excluding the one chosen for the first position) and 21 options for a consonant. If the first letter is a consonant, there are 5 options left for a vowel and 20 options for a consonant.
For the third position, if the second letter is a vowel, there are 4 options left for a vowel and 20 options for a consonant. If the second letter is a consonant, there are 5 options left for a vowel and 19 options for a consonant.
For the fourth position (last letter), there must be a vowel because consecutive letters cannot be the same. Therefore, there are 5 options for a vowel.
To find the total number of possible passwords, we multiply the number of options for each position:
(5 vowels or 21 consonants) (4 vowels or 21 consonants)
(4 vowels or 20 consonants)
(5 vowels) = (5 + 21)
(4 + 21)
(4 + 20)
5 = 26
25
24
5 = 15,600.
Therefore, there are 15,600 different passwords possible.
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