Question:
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?
Solution:
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