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

Question

Philoid · Accepted Answer

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.

The total number of 4 letter codes=10 × 9 × 8 × 7=5040.