Ten books are arranged in a row on a bookshelf. A student has to select three out of these ten books
in such a way that no two books selected by him must have been lying adjacently. In how many
ways can he make the selection?
(a) 56 (b) 64 (c) 72 (d) None of these
option a
ReplyDelete56 values.... take case 10C3 - when all three are together-when two are together..
so thats 120 - 8 -(2*7+7*6) = 120-64 = 56
There is an easier way to solve this.
ReplyDeletea b c are books required
ReplyDeleteremaining books are 7
at least 1 shd be there between them
a 1 b 1 c
Now books remaining are 7-2=5
spaces are 4
Now it becomes
p+q+r+s=5
ans (5+4-1)C3
8C3
so answer is 56
this method is better incase of more complexities in the problem like selecting 4 such that none is consecutive and etc..