4. How many 8-letter code can be formed using the 1st 10 letters of the English
alphabet, if no letter can be repeated?
Answers
Given:-
Number of letters = 10
Find:-
Number of alphabets that formed using first 10 letters of English alaphabet, without repeating.
Solution:-
Let us assume that code is in the form -
Number of 10 letters arranged in 1 box = 10
Number of 10 letters arranged in 2 box = 9
Number of 10 letters arranged in 3 box = 8
Number of 10 letters arranged in 4 box = 7
Number of 10 letters arranged in 5 box = 6
Number of 10 letters arranged in 6 box = 5
Number of 10 letters arranged in 7 box = 4
Number of 10 letters arranged in 8 box = 3
So,
Required number of code of 10 letters and 8 box = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3
=> 1814400
Hence, in 1814400 ways 8-letter code can formed.
Given ,
Repetition of letter is not allowed , so ,
The first place can be filled in 10 different ways by anyone of the first 10 letters of the english alphabet
The second place can be filled in 9 different ways by anyone of the remaining letters
The third place can be filled in 8 different ways by anyone of the remaining letters
Similarly , in 4th , 5th , 6th , 7th and 8th places can be filled in 7,6,5,4,3 different ways by anyone of the remaining letters
Therefore , by multiplication principle
Hence , the required number is 1814400