There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks.
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?
Answer/Solution
246
Steps/Work
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 = >246
Ans D.
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 = >246
Ans D.