Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?	Choose the correct choice from the following.
A) 90	B) 180	C) 360	D) 540	E) 720
3 Blue Marble:   Different distribution : (1) All 3 in the same cup (2) Split 2-1 in two cups (3) Split 1-1-1   Case (1) 3 possibilities   Case (2) 6 possibilities ,   Case (3) 1 possibility   tot. 10 possibilities.   One Green Marble :   3 possibilities (one for each cup at the time)   First Red marble:   3 possibilities (one for each cup at the time)   Second Red marble:   2 possibilities ( because can't go in the same cup with the other Red marble)   TOTAL:   10*3*3*2= 
<gadget id="calculator">10*3*3*2</gadget>
<output>180</output>
180 , answer, 180 .
<result>B</result>
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?