## How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?​

Question

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?​

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1 month 2021-08-16T17:14:55+00:00 2 Answers 0 views 0

Hence, 5040 four-letter codes can be formed using the first 10 letters of the English alphabet, if no letter is repeated.

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How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

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➡️Let the 4 digit code be 1234.

➡️At the first place, the number of letters possible is 10.

➡️Let’s suppose any 1 of the ten occupies place 1.

➡️Now, as the repetition is not allowed, the number of letters possible at place 2 is 9.

➡️Now at 1 and 2, any 2 of the 10 alphabets have been taken.

➡️ The number of alphabets left for place 3 is 8 and similarly the number of alphabets possible at 4 is 7.

➡️Therefore the total number of 4 letter codes=10 × 9 × 8 × 7=5040.

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