Of the science books in a certain supply room, 50 are on botany, 75 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?  Choose one:  A) 81  B) 59  C) 166  D) 285  E) 334
I solve it using the tough luck technique:   According to question: What is the least number of books you should pick so as to get at least 80 books of the same science subject.   80 books of the same science subjects is possible only for two subjects: Physics=90&gt;80 OR Chemistry=110&gt;80   Now, we need to be certain that out of the books we picked, there are either at least 80 physics books or 80 chemistry books   What if we pick the first 80 books and none of them is either Physics or Chemistry. Possible. Thus, we first count all our negatives.   We picked:   50 Botany Books   75 Zoology Books   50 Geology Books   Now, any book we pick will be either Chemistry or Physics. But unfortunately, we can't be lucky enough to pick 80 books and all of them will be Physics, right!!   Thus, in order to make sure that we have 80 books of either of these 2 subjects, we must pick   79*2+1 books   Because, we could have picked the books in following order;   1st book picked: Physics   2nd book picked: Chemistry   3rd book picked: Physics   Thus, Total= 50+75+50+79*2+1=175+1+158= 
<gadget id="calculator">175+1+158</gadget>
<output>334</output>
334   Ans:334
<result>E</result>
Of the science books in a certain supply room, 50 are on botany, 75 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?