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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. The password must contain at least one vowel, one consonant, and one letter that is a repea

A password consists of 4 letters, where each letter can be either a vowel (a, e, i, o, u) or a consonant. The password must contain at least one vowel, one consonant, and one letter that is a repeat of a previous letter. How many different passwords are possible?
 

Option: 1

640
 


Option: 2

850
 


Option: 3

360


Option: 4

840


Answers (1)

best_answer

Case 1: The repeated letter is a vowel:
In this case, we have 5 options for the repeated vowel and 21 options for the consonant (any consonant except the repeated vowel). The remaining two positions can be filled with any vowel or consonant, giving us a total of  5 \times 21 \times 2 \times 2=420  possibilities.

Case 2: The repeated letter is a consonant:
Similarly, we have 21 options for the repeated consonant and 5 options for the vowel (any vowel except the repeated consonant). The remaining two positions can be filled with any vowel or consonant, resulting in a total of 21 \times 5 \times 2 \times 2=420  possibilities.

To find the total number of different passwords, we sum the possibilities from both cases:

420+420=840 .

Therefore, there are 840 different passwords possible.

Posted by

Ritika Harsh

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