In how many ways 5 different balls can be arranged in to 3 different boxes so that no box remains empty?  Select the correct option:
A) 125
B) 150
C) 175
D) 200
E) 225
1. The total number of possibilities including empty boxes: 35=24335=243   2. Two of the boxes are empty: C32=3C23=3   3. One but not two of the boxes is empty: 3∗(25−2)=903∗(25−2)=90   4. the total number of possibilities excluding empty boxes:  243 - 3 - 90= 
<gadget id="calculator"> 243 - 3 - 90</gadget>
<output>150</output>
150   ANS:150
<result>B</result>
In how many ways 5 different balls can be arranged in to 3 different boxes so that no box remains empty?