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

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

Suppose the

$4$

-digit code to be $1234$ .

So, in the first place, the number of possible alphabets is $10$ .

Since repetition is not allowed then the number of alphabets left for the second letter is $9$ .

Similarly, the number of alphabets left for the third letter is $8$ .

And the number of alphabets left for the fourth letter is $7$ .

Hence, the total number of $4$ – letter code that can be formed using the first $10$ letters of the English alphabet without repetition

$=10\text{ }\times \text{ }9\text{ }\times \text{ }8\text{ }\times \text{ }7$

$=5040$ .

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