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Asked by Piyush Last Modified
Answer 
Harshit Bhardwaj
There are as many codes as there are ways of filling 4 vacant places 
in succession by the first 10 letters of the English alphabet, keeping in mind that the repetition of letters is not allowed.
The first place can be filled in 10 different ways by any of the first 10 letters of the English alphabet following which, the second place can be filled in by any of the remaining letters in 9 different ways. The third place can be filled in by any of the remaining 8 letters in 8 different ways and the fourth place can be filled in by any of the remaining 7 letters in 7 different ways.
Therefore, by multiplication principle, the required numbers of ways in which 4 vacant places can be filled is 10 × 9 × 8 × 7 = 5040
Hence, 5040 four-letter codes can be formed using the first 10 letters of the English alphabet, if no letter is repeated.
read lessThe first letter of the code word can be selected in 10 ways. After the selection of the first letter, we have nine letters. Hence the second letter can be chosen in 9 ways. According to FPC, first two letters can be selected in 10×910×9 ways
Similarly, the third letter can be selected in 8 ways. Under the fourth letter can be chosen in 7 ways. According to FPC, a number of ways of selecting four letters out of 10 letters of the English alphabet.
⇒10×9×8×7⇒10×9×8×7ways
⇒5040⇒5040ways
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