How many ways can 5 different colored marbles be placed in 3 distinct pockets such that any pocket contains at least 1 marble?  Pick one
A) 60  B) 90  C) 120  D) 150  E) 180
With 3,1,1 distribution:   # of ways to select 3 from 5   5!/3!2! = 10   # of ways to select 1 ball from 2   2!/1! = 2   # of ways to select 1 ball from 1   1!/1! 2 /1= 
<gadget id="calculator">2 /1</gadget>
<output>2</output>
2   # of ways to select 1 ball from 1   1!/1! = 1   How many ways to distribute 3,1 and 1 to 3 boxes? 3!/2! 1 /1= 
<gadget id="calculator">1 /1</gadget>
<output>1</output>
1   How many ways to distribute 3,1 and 1 to 3 boxes? 3!/2!= 3   10*2*3= 
<gadget id="calculator">10*2*3</gadget>
<output>60</output>
60   With 2,2,1 distribution:   How many ways to select 2 from 5?   5!/2!3!= 10   # of ways to select 2 from 3   3!/2!1! = 3   # of ways to select 1 from 1   1   How many ways to distribute 2,2,1 to 3 boxes? 3!/2! = 3   10*3*3= 
<gadget id="calculator">10*3*3</gadget>
<output>90</output>
90   90+60= 
<gadget id="calculator">90+60</gadget>
<output>150</output>
150   Answer: 150. 150
<result>D</result>
How many ways can 5 different colored marbles be placed in 3 distinct pockets such that any pocket contains at least 1 marble?