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  • A code consists of 5 letters chosen from the English alphabet (26 letters), where repetition is allowed. However, the code must not contain any vowels (a, e, i, o, u). Ho

A code consists of 5 letters chosen from the English alphabet (26 letters), where repetition is allowed. However, the code must not contain any vowels (a, e, i, o, u). How many different codes are possible?

 

Option: 1

3,789,568

 


Option: 2

9,563,125

 


Option: 3

5,025,120

 


Option: 4

4,084,101


Answers (1)

best_answer

To calculate the number of different codes that can be formed with 5 letters from the English alphabet, where repetition is allowed and the code must not contain any vowels, we need to consider the available options for each letter position.

Since we have 26 letters in the English alphabet and we want to exclude the 5 vowels (a, e, i, o, u), we have 21 remaining consonant letters.

For each position in the code, we have 21 options (the consonant letters) to choose from.

Since repetition is allowed, we have 21 choices for each of the 5 positions.

Therefore, the total number of different codes possible is:

21 \times 21 \times 21 \times 21 \times 21=21^5=4,084,101 .
Therefore, there are 4,084,101 different codes that can be formed with 5 letters from the English alphabet, where repetition is allowed and the code does not contain any vowels.

Posted by

Rakesh

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