How many different selections of 6 books can be made from 11 different books, if
(i) two particular books are always selected.
(ii) two particular books are never selected?

Explanation

(i) Since, two particular books are always selected. It means that 6y-2=4 books are selected out of the remaining 11-2=9 books.
`therefore`Required number of ways`=.^(9)C_(4)=(9*8*7*6)/(1*2*3*4)=126`.
(ii) Since, two particular books are never selected, it means that 6 books are selected out of the remaining 11-2=9 books.
`therefore` Required number of ways=`.^(9)C_(6)`
`=.^(9)C_(3)=(9*8*7)/(1*2*3)=84`.