Question

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

Answer 1

Here, the unit place can be filled by any one of the first 10 letters of the English alphabet. So the unit place can be filled in 10 ways. The tens place can be filled in 9 ways by remaining 9 letters of the English alphabet. The hundreds place can be filled in 8 ways by remaining 8 letters of the English alphabet.

The thousands place can be filled in 7 ways by the remaining 7 letters of the English alphabet.

$\therefore$ Total number of 4-letter code = $7\times 8\times 9\times 10=5040.$