How many different selections of 4 books can be made from 10 different books, if
(i) there is no restriction?
(ii) two particular books are always selected?
(iii) two particular books are never selected?
Since there are 10 different books out of which 4 is to be selected .
(i) When there is no restriction
No. of ways in which 4 books be selected $={ }^{10} \mathrm{C}_{4}$
= 210 ways
(ii) Two particular books are always selected
Since two particular books are always selected, so ways of selecting 2 books from 8 are $={ }^{8} C_{2}$ ways
= 28 ways
(iii) Two particular books are never selected
Since two particular books are never selected so, ways of selecting 4 books from 8 are $={ }^{8} \mathrm{C}_{4}$ ways
= 70 ways
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