Question

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

Answer 1

First ten letters of the alphabet can be used i.e A,B, C,D,E, F,G,H, I,J.
Four letter code is to be formed.
$\square \square \square \square$
The first place (from left) can be filled by using any of the 10 alphabets. So, there are 10 ways to fill first place.
Since, repetition is not allowed . So, second place can be filled by remaining 9 alphabets.
So, there are 9 ways to fill second place.
Similarly, third place can be filled by remaining 8 alphabets.
And fourth place can be filled by remaining 7 alphabets.
Hence, the required number of ways in which four letter code can be formed is $10\times 9\times 8\times 7=5040$