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How many 5-letter codes can be formed using the first 7 letters of the English alphabet, if no letters can be repeated?

Option: 1

5040
 


Option: 2

760


Option: 3

840

 


Option: 4

2520


Answers (1)

best_answer

Given that,

Forming a five letters code using the first 7 letters of the English alphabet and the repetition of letters is now allowed.

The first place can be filled in 7 different ways by any of the 7 letters of the English alphabet.

The second place can be filled in by any of the remaining letters in 6 different ways.

The third place can be filled in by any of the remaining letters in 5 different ways.

The fourth place can be filled in by any of the remaining letters in 4 different ways.

The fifth place can be filled in by any of the remaining letters in 3 different ways.

Thus, by using the multiplication principle, the required number of ways in which 5-letter code can be filled is7\times 6\times 5\times 4\times 3=2520.

Therefore, the required number of ways in which a 5-letter code can be filled by 2520 ways.

Posted by

Devendra Khairwa

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