There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback? Choices.
A) 75
B) 120
C) 210
D) 246
E) 252
Paperbacks - 4, hardbacks - 6   5 books in total and at least 1 from each.   Total combinations for 5 books = (1pb, 4 hb) + (4pb, 1hb) + (3pb, 2hb) + (2pb, 3hb)   1pb, 4hb = 4c1*6c4 = 60   4pb,1hb = 4c4*6c1 = 6   3pb,2hb = 4c3*6c2 = 60   2pb,3hb = 4c2*6c3 = 120   Total combinations of 5 books = 60+6+60+120= 
<gadget id="calculator">60+6+60+120</gadget>
<output>246</output>
&gt;246   Ans 246.
<result>D</result>
There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback?