Suppose we have six marbles: 3 yellow 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. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
Choose the correct option.
A) 180
B) 160
C) 149
D) 150
E) 175
# ways to distribute yellow marbels(3) is :   1 in each cup= 1   2 in one cup and 1 in other=6   all 3 in one cup = 3   total 1+6+3= 
<gadget id="calculator">1+6+3</gadget>
<output>10</output>
10 possibilities   # ways to distribute Red marbels(2) is :   1 in each cup= 3 ways   all in one cup = 3ways   total 6ways.   # ways to distribute Green marbels(1) is :   3 ways   total number of ways = 10*6 *3= 
<gadget id="calculator">10*6 *3</gadget>
<output>180</output>
180   180
<result>A</result>
Suppose we have six marbles: 3 yellow 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. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?