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

Options

A. 35
B. 30
C. 50
D. 60

Answer

A

Explanation

Let '1' be associated with 'r', `r in{1,2,3,4,5},` then '2' can be associated with r,r+1, . . ,5. let '2' be associated with 'j' then 3 can be associated with j,j+1, . . ,5. thus, required number of fucntions
`underset(r=1)overset(5)(sum)(underset(j=r)overset(5)(sum)(6-j))=underset(r=1)overset(5)(sum)((6-r)(7-r))/(2)=35`