there are 8 books on a shelf, of which 3 are paperbacks and 5 are hardbacks. how many possible selections of 4 books from this shelf include at least one paperback?
Choose the correct choice
A) 40  B) 45  C) 50  D) 55  E) 65
<gadget id="calculator">binomial(8, 4)</gadget>
<output>70</output>

<gadget id="calculator">binomial(5, 4)</gadget>
<output>5</output>

<gadget id="calculator">70 - 5</gadget>
<output>65</output>

<result>E</result>
there are 8 books on a shelf, of which 3 are paperbacks and 5 are hardbacks. how many possible selections of 4 books from this shelf include at least one paperback?
subtract(choose(8, 4), choose(5, 4))
approach 1 at - least 1 paper back = total - no paper back 8 c 4 - 5 c 4 = 65 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 5 c 3 + 3 c 2 * 5 c 2 + 3 c 3 * 5 c 1 = 65 answer is e