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How many 4 - letter code can be formed u...

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

A

35

B

30

C

50

D

60

Text Solution

Verified by Experts

The correct Answer is:
A
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`
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